detailed information: The input equation set is:
 | | | | | | -10 | A | + | | 10 | B | + | | 4 | C | = | | -20 | | (4) |
| | | Question solving process:
Multiply both sides of equation (1) by 10, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 20, the equation can be obtained: , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 10, the equation can be obtained: , then subtract both sides of equation (9) from both sides of equation (6), the equations are reduced to:
交After the exchange of equation (3) and equation (4), the equation system becomes:
Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 17, the equation can be obtained: , then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (3) by 5 Divide the two sides of equation (3) by 17, the equation can be obtained: | | 10 | C | + | | | 100 17 | D | = | | - | 100 17 | (11) | , then add the two sides of equation (11) to both sides of equation (6), the equations are reduced to:
 | | | | | | | | - | 206 17 | D | + | | 2 | F | = | | - | 780 17 | | (6) |
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Multiply both sides of equation (4) by 176 Divide the two sides of equation (4) by 17, the equation can be obtained: | - | 176 17 | D | + | | | 176 17 | E | | - | 176 17 | F | = | | 0 | (12) | , then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
 | | | | | | | | | 312 17 | E | | - | 176 17 | F | = | | | 300 17 | | (5) |
| - | 206 17 | D | + | | 2 | F | = | | - | 780 17 | | (6) |
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Multiply both sides of equation (4) by 206 Divide the two sides of equation (4) by 17, the equation can be obtained: | - | 206 17 | D | + | | | 206 17 | E | | - | 206 17 | F | = | | 0 | (13) | , then subtract both sides of equation (13) from both sides of equation (6), the equations are reduced to:
 | | | | | | | | | 312 17 | E | | - | 176 17 | F | = | | | 300 17 | | (5) |
| - | 206 17 | E | + | | | 240 17 | F | = | | - | 780 17 | | (6) |
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Multiply both sides of equation (5) by 103 Divide the two sides of equation (5) by 156, the equation can be obtained: | | | 206 17 | E | | - | 4532 663 | F | = | | | 2575 221 | (14) | , then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
 | | | | | | | | | 312 17 | E | | - | 176 17 | F | = | | | 300 17 | | (5) |
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Multiply both sides of equation (6) by 1716 Divide both sides of equation (6) by 1207, get the equation: | | | 12496 1207 | F | = | | - | 58740 1207 | (15) | , then add the two sides of equation (15) to both sides of equation (5), get the equation:
Multiply both sides of equation (6) by 39 Divide both sides of equation (6) by 284, get the equation:, then add the two sides of equation (16) to both sides of equation (4), get the equation:
Multiply both sides of equation (5) by 17 Divide both sides of equation (5) by 312, get the equation:, then subtract both sides of equation (17) from both sides of equation (4), get the equation:
Multiply both sides of equation (4) by 20, get the equation:, then add the two sides of equation (18) to both sides of equation (3), get the equation:
Add both sides of equation (4) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 34, get the equation:, then subtract both sides of equation (19) from both sides of equation (2), get the equation:
Divide both sides of equation (3) by 34, get the equation:, then subtract both sides of equation (20) from both sides of equation (1), get the equation:
Add both sides of equation (2) to 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》 |