detailed information: The input equation set is:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | A | + | | 120 | B | + | | 10 | C | + | | 90 | D | + | | 1200 | E | + | | 10800 | F | + | | 900 | G | + | | 108000 | H | = | | 3 | | (2) |
| | A | + | | 120 | B | + | | 20 | C | + | | D | + | | 2400 | E | + | | 120 | F | + | | 20 | G | + | | 2400 | H | = | | 2 | | (3) |
| | A | + | | 120 | B | + | | 20 | C | + | | 90 | D | + | | 2400 | E | + | | 10800 | F | + | | 1800 | G | + | | 216000 | H | = | | 4 | | (4) |
| | A | + | | 240 | B | + | | 10 | C | + | | D | + | | 2400 | E | + | | 240 | F | + | | 10 | G | + | | 2400 | H | = | | 5 | | (5) |
| | A | + | | 240 | B | + | | 10 | C | + | | 90 | D | + | | 2400 | E | + | | 21600 | F | + | | 900 | G | + | | 216000 | H | = | | 7 | | (6) |
| | A | + | | 240 | B | + | | 20 | C | + | | D | + | | 4800 | E | + | | 240 | F | + | | 20 | G | + | | 4800 | H | = | | 6 | | (7) |
| | A | + | | 240 | B | + | | 20 | C | + | | 90 | D | + | | 4800 | E | + | | 21600 | F | + | | 1800 | G | + | | 432000 | H | = | | 8 | | (8) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (2) |
| | A | + | | 120 | B | + | | 20 | C | + | | D | + | | 2400 | E | + | | 120 | F | + | | 20 | G | + | | 2400 | H | = | | 2 | | (3) |
| | A | + | | 120 | B | + | | 20 | C | + | | 90 | D | + | | 2400 | E | + | | 10800 | F | + | | 1800 | G | + | | 216000 | H | = | | 4 | | (4) |
| | A | + | | 240 | B | + | | 10 | C | + | | D | + | | 2400 | E | + | | 240 | F | + | | 10 | G | + | | 2400 | H | = | | 5 | | (5) |
| | A | + | | 240 | B | + | | 10 | C | + | | 90 | D | + | | 2400 | E | + | | 21600 | F | + | | 900 | G | + | | 216000 | H | = | | 7 | | (6) |
| | A | + | | 240 | B | + | | 20 | C | + | | D | + | | 4800 | E | + | | 240 | F | + | | 20 | G | + | | 4800 | H | = | | 6 | | (7) |
| | A | + | | 240 | B | + | | 20 | C | + | | 90 | D | + | | 4800 | E | + | | 21600 | F | + | | 1800 | G | + | | 432000 | H | = | | 8 | | (8) |
|
Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | A | + | | 120 | B | + | | 20 | C | + | | 90 | D | + | | 2400 | E | + | | 10800 | F | + | | 1800 | G | + | | 216000 | H | = | | 4 | | (4) |
| | A | + | | 240 | B | + | | 10 | C | + | | D | + | | 2400 | E | + | | 240 | F | + | | 10 | G | + | | 2400 | H | = | | 5 | | (5) |
| | A | + | | 240 | B | + | | 10 | C | + | | 90 | D | + | | 2400 | E | + | | 21600 | F | + | | 900 | G | + | | 216000 | H | = | | 7 | | (6) |
| | A | + | | 240 | B | + | | 20 | C | + | | D | + | | 4800 | E | + | | 240 | F | + | | 20 | G | + | | 4800 | H | = | | 6 | | (7) |
| | A | + | | 240 | B | + | | 20 | C | + | | 90 | D | + | | 4800 | E | + | | 21600 | F | + | | 1800 | G | + | | 432000 | H | = | | 8 | | (8) |
|
Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | A | + | | 240 | B | + | | 10 | C | + | | D | + | | 2400 | E | + | | 240 | F | + | | 10 | G | + | | 2400 | H | = | | 5 | | (5) |
| | A | + | | 240 | B | + | | 10 | C | + | | 90 | D | + | | 2400 | E | + | | 21600 | F | + | | 900 | G | + | | 216000 | H | = | | 7 | | (6) |
| | A | + | | 240 | B | + | | 20 | C | + | | D | + | | 4800 | E | + | | 240 | F | + | | 20 | G | + | | 4800 | H | = | | 6 | | (7) |
| | A | + | | 240 | B | + | | 20 | C | + | | 90 | D | + | | 4800 | E | + | | 21600 | F | + | | 1800 | G | + | | 432000 | H | = | | 8 | | (8) |
|
Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (5) |
| | A | + | | 240 | B | + | | 10 | C | + | | 90 | D | + | | 2400 | E | + | | 21600 | F | + | | 900 | G | + | | 216000 | H | = | | 7 | | (6) |
| | A | + | | 240 | B | + | | 20 | C | + | | D | + | | 4800 | E | + | | 240 | F | + | | 20 | G | + | | 4800 | H | = | | 6 | | (7) |
| | A | + | | 240 | B | + | | 20 | C | + | | 90 | D | + | | 4800 | E | + | | 21600 | F | + | | 1800 | G | + | | 432000 | H | = | | 8 | | (8) |
|
Subtract both sides of equation (1) from both sides of equation (6) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (5) |
| | 120 | B | + | | 89 | D | + | | 1200 | E | + | | 21480 | F | + | | 890 | G | + | | 214800 | H | = | | 6 | | (6) |
| | A | + | | 240 | B | + | | 20 | C | + | | D | + | | 4800 | E | + | | 240 | F | + | | 20 | G | + | | 4800 | H | = | | 6 | | (7) |
| | A | + | | 240 | B | + | | 20 | C | + | | 90 | D | + | | 4800 | E | + | | 21600 | F | + | | 1800 | G | + | | 432000 | H | = | | 8 | | (8) |
|
Subtract both sides of equation (1) from both sides of equation (7) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (5) |
| | 120 | B | + | | 89 | D | + | | 1200 | E | + | | 21480 | F | + | | 890 | G | + | | 214800 | H | = | | 6 | | (6) |
| | 120 | B | + | | 10 | C | + | | 3600 | E | + | | 120 | F | + | | 10 | G | + | | 3600 | H | = | | 5 | | (7) |
| | A | + | | 240 | B | + | | 20 | C | + | | 90 | D | + | | 4800 | E | + | | 21600 | F | + | | 1800 | G | + | | 432000 | H | = | | 8 | | (8) |
|
Subtract both sides of equation (1) from both sides of equation (8) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (5) |
| | 120 | B | + | | 89 | D | + | | 1200 | E | + | | 21480 | F | + | | 890 | G | + | | 214800 | H | = | | 6 | | (6) |
| | 120 | B | + | | 10 | C | + | | 3600 | E | + | | 120 | F | + | | 10 | G | + | | 3600 | H | = | | 5 | | (7) |
| | 120 | B | + | | 10 | C | + | | 89 | D | + | | 3600 | E | + | | 21480 | F | + | | 1790 | G | + | | 430800 | H | = | | 7 | | (8) |
|
交After the exchange of equation (2) and equation (5), the equation system becomes:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (5) |
| | 120 | B | + | | 89 | D | + | | 1200 | E | + | | 21480 | F | + | | 890 | G | + | | 214800 | H | = | | 6 | | (6) |
| | 120 | B | + | | 10 | C | + | | 3600 | E | + | | 120 | F | + | | 10 | G | + | | 3600 | H | = | | 5 | | (7) |
| | 120 | B | + | | 10 | C | + | | 89 | D | + | | 3600 | E | + | | 21480 | F | + | | 1790 | G | + | | 430800 | H | = | | 7 | | (8) |
|
Subtract both sides of equation (2) from both sides of equation (6) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (5) |
| | 89 | D | + | | 21360 | F | + | | 890 | G | + | | 213600 | H | = | | 2 | | (6) |
| | 120 | B | + | | 10 | C | + | | 3600 | E | + | | 120 | F | + | | 10 | G | + | | 3600 | H | = | | 5 | | (7) |
| | 120 | B | + | | 10 | C | + | | 89 | D | + | | 3600 | E | + | | 21480 | F | + | | 1790 | G | + | | 430800 | H | = | | 7 | | (8) |
|
Subtract both sides of equation (2) from both sides of equation (7) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (5) |
| | 89 | D | + | | 21360 | F | + | | 890 | G | + | | 213600 | H | = | | 2 | | (6) |
| | 10 | C | + | | 2400 | E | + | | 10 | G | + | | 2400 | H | = | | 1 | | (7) |
| | 120 | B | + | | 10 | C | + | | 89 | D | + | | 3600 | E | + | | 21480 | F | + | | 1790 | G | + | | 430800 | H | = | | 7 | | (8) |
|
Subtract both sides of equation (2) from both sides of equation (8) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 10 | C | + | | 89 | D | + | | 1200 | E | + | | 10680 | F | + | | 1790 | G | + | | 214800 | H | = | | 3 | | (4) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (5) |
| | 89 | D | + | | 21360 | F | + | | 890 | G | + | | 213600 | H | = | | 2 | | (6) |
| | 10 | C | + | | 2400 | E | + | | 10 | G | + | | 2400 | H | = | | 1 | | (7) |
| | 10 | C | + | | 89 | D | + | | 2400 | E | + | | 21360 | F | + | | 1790 | G | + | | 429600 | H | = | | 3 | | (8) |
|
Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (5) |
| | 89 | D | + | | 21360 | F | + | | 890 | G | + | | 213600 | H | = | | 2 | | (6) |
| | 10 | C | + | | 2400 | E | + | | 10 | G | + | | 2400 | H | = | | 1 | | (7) |
| | 10 | C | + | | 89 | D | + | | 2400 | E | + | | 21360 | F | + | | 1790 | G | + | | 429600 | H | = | | 3 | | (8) |
|
Subtract both sides of equation (3) from both sides of equation (7) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (5) |
| | 89 | D | + | | 21360 | F | + | | 890 | G | + | | 213600 | H | = | | 2 | | (6) |
| | | 10 | C | + | | 89 | D | + | | 2400 | E | + | | 21360 | F | + | | 1790 | G | + | | 429600 | H | = | | 3 | | (8) |
|
Subtract both sides of equation (3) from both sides of equation (8) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | 89 | D | + | | 10680 | F | + | | 890 | G | + | | 106800 | H | = | | 2 | | (5) |
| | 89 | D | + | | 21360 | F | + | | 890 | G | + | | 213600 | H | = | | 2 | | (6) |
| | | 89 | D | + | | 1200 | E | + | | 21360 | F | + | | 1780 | G | + | | 428400 | H | = | | 2 | | (8) |
|
Subtract both sides of equation (4) from both sides of equation (5) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | | 89 | D | + | | 21360 | F | + | | 890 | G | + | | 213600 | H | = | | 2 | | (6) |
| | | 89 | D | + | | 1200 | E | + | | 21360 | F | + | | 1780 | G | + | | 428400 | H | = | | 2 | | (8) |
|
Subtract both sides of equation (4) from both sides of equation (6) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | | | | 89 | D | + | | 1200 | E | + | | 21360 | F | + | | 1780 | G | + | | 428400 | H | = | | 2 | | (8) |
|
Subtract both sides of equation (4) from both sides of equation (8) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | | | | 1200 | E | + | | 10680 | F | + | | 214800 | H | = | | 0 | | (8) |
|
交After the exchange of equation (5) and equation (7), the equation system becomes:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | | | | 1200 | E | + | | 10680 | F | + | | 214800 | H | = | | 0 | | (8) |
|
Subtract both sides of equation (5) from both sides of equation (8) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | | | |
Subtract both sides of equation (6) from both sides of equation (8) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
| | | | |
Add both sides of equation (7) to both sides of equation (8) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
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Add both sides of equation (8) to both sides of equation (7), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
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Divide both sides of equation (8) by 89, get the equation:, then subtract both sides of equation (9) from both sides of equation (5), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | + | | 213600 | H | = | | 2 | | (4) |
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Multiply both sides of equation (8) by 2, get the equation:, then subtract both sides of equation (10) from both sides of equation (4), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | + | | 1200 | H | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | = | | 2 | | (4) |
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Divide both sides of equation (8) by 89, get the equation:, then subtract both sides of equation (11) from both sides of equation (3), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | + | | 1200 | H | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | = | | 2 | | (4) |
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Divide both sides of equation (8) by 89, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | + | | 1200 | H | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | = | | 2 | | (4) |
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Divide both sides of equation (8) by 89, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | = | | 2 | | (4) |
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Subtract both sides of equation (7) from both sides of equation (6), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | = | | 1 | | (3) |
| | 89 | D | + | | 10680 | F | + | | 1780 | G | = | | 2 | | (4) |
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Multiply both sides of equation (7) by 2, get the equation:, then add the two sides of equation (14) to both sides of equation (4), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | = | | 4 | | (2) |
| | 10 | C | + | | 1200 | E | + | | 10 | G | = | | 1 | | (3) |
| | | | | |
Divide both sides of equation (7) by 89, get the equation:, then add the two sides of equation (15) to both sides of equation (3), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | + | | 10 | G | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | = | | 4 | | (2) |
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Divide both sides of equation (7) by 89, get the equation:, then add the two sides of equation (16) to both sides of equation (1), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | = | | 4 | | (2) |
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Subtract both sides of equation (6) from both sides of equation (4), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | = | | 1 | | (1) |
| | 120 | B | + | | 1200 | E | + | | 120 | F | = | | 4 | | (2) |
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Divide both sides of equation (6) by 89, get the equation:, then subtract both sides of equation (17) from both sides of equation (2), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | + | | 120 | F | = | | 1 | | (1) |
| | | | | | | |
Divide both sides of equation (6) by 89, get the equation:, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | = | | 1 | | (1) |
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Subtract both sides of equation (5) from both sides of equation (3), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | = | | 1 | | (1) |
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Subtract both sides of equation (5) from both sides of equation (2), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | + | | 1200 | E | = | | 1 | | (1) |
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Subtract both sides of equation (5) from both sides of equation (1), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | D | = | | 1 | | (1) |
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Divide both sides of equation (4) by 89, get the equation:, then subtract both sides of equation (19) from both sides of equation (1), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | = | | | 87 89 | | (1) |
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Subtract both sides of equation (3) from both sides of equation (1), get the equation:
Subtract both sides of equation (2) from both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |