detailed information: The input equation set is:
| | | | | 4 25 | A | | - | 12 125 | B | + | | | 12 125 | C | | - | 27309 100 | D | = | | | 127909 100 | | (1) |
| | | 9 100 | A | | - | 9 100 | B | + | | | 9 100 | C | | - | 27309 100 | D | = | | | 183709 100 | | (2) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 27309 100 | D | = | | | 239609 100 | | (3) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 27309 100 | D | = | | | 295409 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 | | - | 245781 1600 | D | = | | | 1151181 1600 | (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 | | - | 27309 100 | D | = | | | 127909 100 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 1788163 1600 | | (2) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 27309 100 | D | = | | | 239609 100 | | (3) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 27309 100 | D | = | | | 295409 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 | | - | 245781 1600 | D | = | | | 1151181 1600 | (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 | | - | 27309 100 | D | = | | | 127909 100 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 1788163 1600 | | (2) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 2682563 1600 | | (3) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 27309 100 | D | = | | | 295409 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 | | - | 245781 1600 | D | = | | | 1151181 1600 | (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 | | - | 27309 100 | D | = | | | 127909 100 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 1788163 1600 | | (2) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 2682563 1600 | | (3) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 3575363 1600 | | (4) |
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Multiply both sides of equation (2) by 4, the equation can be obtained: | - | 18 125 | B | + | | | 18 125 | C | | - | 191163 400 | D | = | | | 1788163 400 | (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 | | - | 27309 100 | D | = | | | 127909 100 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 1788163 1600 | | (2) |
| | | 9 50 | C | | - | 191163 320 | D | = | | | 1967043 320 | | (3) |
| | | 18 125 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 3575363 1600 | | (4) |
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Multiply both sides of equation (2) by 4, the equation can be obtained: | - | 18 125 | B | + | | | 18 125 | C | | - | 191163 400 | D | = | | | 1788163 400 | (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 | | - | 27309 100 | D | = | | | 127909 100 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 1788163 1600 | | (2) |
| | | 9 50 | C | | - | 191163 320 | D | = | | | 1967043 320 | | (3) |
| | | 9 50 | C | | - | 191163 320 | D | = | | | 2145603 320 | | (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 | | - | 27309 100 | D | = | | | 127909 100 | | (1) |
| - | 9 250 | B | + | | | 9 250 | C | | - | 191163 1600 | D | = | | | 1788163 1600 | | (2) |
| | | 9 50 | C | | - | 191163 320 | D | = | | | 1967043 320 | | (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》 |