detailed information: The input equation set is:
| | | | | | 100 | B | + | | 220 | C | + | | 510 | D | = | | -10 | | (3) |
| | 150 | A | + | | 220 | C | + | | 510 | D | = | | -25 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 150, the equation can be obtained: | | 150 | A | + | | 150 | B | + | | 150 | C | = | | 0 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 100 | B | + | | 220 | C | + | | 510 | D | = | | -10 | | (3) |
| | 150 | A | + | | 220 | C | + | | 510 | D | = | | -25 | | (4) |
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Multiply both sides of equation (1) by 150, the equation can be obtained: | | 150 | A | + | | 150 | B | + | | 150 | C | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
| | | | | | 100 | B | + | | 220 | C | + | | 510 | D | = | | -10 | | (3) |
| -150 | B | + | | 70 | C | + | | 510 | D | = | | -25 | | (4) |
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Multiply both sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
| | | | | | -150 | B | + | | 70 | C | + | | 510 | D | = | | -25 | | (4) |
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Multiply both sides of equation (2) by 3, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (3) by 13 Divide the two sides of equation (3) by 2, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (4) by 2 Divide both sides of equation (4) by 15, get the equation:, then subtract both sides of equation (10) from both sides of equation (3), get the equation:
Multiply both sides of equation (3) by 15 Divide both sides of equation (3) by 8, get the equation:, then subtract both sides of equation (11) from both sides of equation (2), get the equation:
Divide both sides of equation (3) by 80, get the equation:, then add the two sides of equation (12) to both sides of equation (1), get the equation:
Divide both sides of equation (2) by 50, get the equation:, then add the two sides of equation (13) 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》 |