detailed information: The input equation set is:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | -1 | D | = | | | 512 125 | | (1) |
| | | 9 100 | A | | - | 9 100 | B | + | | | 9 100 | C | | -1 | D | = | | | 609 100 | | (2) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | -1 | D | = | | | 809 100 | | (3) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | -1 | D | = | | | 1009 100 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 9 100 | A | | - | 27 500 | B | + | | | 27 500 | C | | - | 9 16 | D | = | | | 288 125 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | -1 | D | = | | | 512 125 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 1893 500 | | (2) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | -1 | D | = | | | 809 100 | | (3) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | -1 | D | = | | | 1009 100 | | (4) |
|
Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 9 100 | A | | - | 27 500 | B | + | | | 27 500 | C | | - | 9 16 | D | = | | | 288 125 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | -1 | D | = | | | 512 125 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 1893 500 | | (2) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 2893 500 | | (3) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | -1 | D | = | | | 1009 100 | | (4) |
|
Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 9 100 | A | | - | 27 500 | B | + | | | 27 500 | C | | - | 9 16 | D | = | | | 288 125 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | -1 | D | = | | | 512 125 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 1893 500 | | (2) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 2893 500 | | (3) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 3893 500 | | (4) |
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Multiply both sides of equation (2) by 4, the equation can be obtained: | - | 18 125 | B | + | | | 18 125 | C | | - | 7 4 | D | = | | | 1893 125 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | -1 | D | = | | | 512 125 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 1893 500 | | (2) |
| | | 9 50 | C | | - | 35 16 | D | = | | | 2093 100 | | (3) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 3893 500 | | (4) |
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Multiply both sides of equation (2) by 4, the equation can be obtained: | - | 18 125 | B | + | | | 18 125 | C | | - | 7 4 | D | = | | | 1893 125 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | -1 | D | = | | | 512 125 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 1893 500 | | (2) |
| | | 9 50 | C | | - | 35 16 | D | = | | | 2093 100 | | (3) |
| | | 9 50 | C | | - | 35 16 | D | = | | | 2293 100 | | (4) |
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Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | -1 | D | = | | | 512 125 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 7 16 | D | = | | | 1893 500 | | (2) |
| | | 9 50 | C | | - | 35 16 | D | = | | | 2093 100 | | (3) |
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由第(4)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |