detailed information: The input equation set is:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | A | + | | 120 | B | + | | 20 | C | + | | 2400 | D | = | | 2 | | (2) |
| | A | + | | 180 | B | + | | 10 | C | + | | 1800 | D | = | | 3 | | (3) |
| | A | + | | 180 | B | + | | 20 | C | + | | 3600 | D | = | | 4 | | (4) |
| 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 | + | | 1200 | D | = | | 1 | | (1) |
| | | A | + | | 180 | B | + | | 10 | C | + | | 1800 | D | = | | 3 | | (3) |
| | A | + | | 180 | B | + | | 20 | C | + | | 3600 | D | = | | 4 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | | | A | + | | 180 | B | + | | 20 | C | + | | 3600 | D | = | | 4 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | | | 60 | B | + | | 10 | C | + | | 2400 | D | = | | 3 | | (4) |
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交After the exchange of equation (2) and equation (3), the equation system becomes:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | | | 60 | B | + | | 10 | C | + | | 2400 | D | = | | 3 | | (4) |
|
Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | | |
Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | | |
Multiply both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (5) from both sides of equation (3), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | | |
Subtract both sides of equation (4) from both sides of equation (2), get the equation:
 | | | | A | + | | 120 | B | + | | 10 | C | + | | 1200 | D | = | | 1 | | (1) |
| | | |
Multiply both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (6) from both sides of equation (1), get the equation:
Subtract both sides of equation (3) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 2, get the equation:, then subtract both sides of equation (7) 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》 |