detailed information: The input equation set is:
| | | | | 387 100 | A | + | | | 67 25 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (1) |
| | | 13 10 | A | + | | | 3 10 | B | + | | | 3 10 | C | + | | | 3 10 | D | = | | | 3 10 | | (2) |
| | | 23 10 | A | + | | | 13 10 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (3) |
| | | 3 10 | A | + | | | 3 10 | B | + | | | 3 10 | C | + | | | 3 10 | D | = | | | 3 10 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 130 Divide the two sides of equation (1) by 387, the equation can be obtained: | | | 13 10 | A | + | | | 1742 1935 | B | + | | | 169 387 | C | + | | | 169 387 | D | = | | | 13 129 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | 387 100 | A | + | | | 67 25 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (1) |
| - | 2323 3870 | B | | - | 529 3870 | C | | - | 529 3870 | D | = | | | 257 1290 | | (2) |
| | | 23 10 | A | + | | | 13 10 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (3) |
| | | 3 10 | A | + | | | 3 10 | B | + | | | 3 10 | C | + | | | 3 10 | D | = | | | 3 10 | | (4) |
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Multiply both sides of equation (1) by 230 Divide the two sides of equation (1) by 387, the equation can be obtained: | | | 23 10 | A | + | | | 3082 1935 | B | + | | | 299 387 | C | + | | | 299 387 | D | = | | | 23 129 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | 387 100 | A | + | | | 67 25 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (1) |
| - | 2323 3870 | B | | - | 529 3870 | C | | - | 529 3870 | D | = | | | 257 1290 | | (2) |
| - | 1133 3870 | B | + | | | 2041 3870 | C | + | | | 2041 3870 | D | = | | | 157 1290 | | (3) |
| | | 3 10 | A | + | | | 3 10 | B | + | | | 3 10 | C | + | | | 3 10 | D | = | | | 3 10 | | (4) |
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Multiply both sides of equation (1) by 10 Divide the two sides of equation (1) by 129, the equation can be obtained: | | | 3 10 | A | + | | | 134 645 | B | + | | | 13 129 | C | + | | | 13 129 | D | = | | | 1 43 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | 387 100 | A | + | | | 67 25 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (1) |
| - | 2323 3870 | B | | - | 529 3870 | C | | - | 529 3870 | D | = | | | 257 1290 | | (2) |
| - | 1133 3870 | B | + | | | 2041 3870 | C | + | | | 2041 3870 | D | = | | | 157 1290 | | (3) |
| | | 119 1290 | B | + | | | 257 1290 | C | + | | | 257 1290 | D | = | | | 119 430 | | (4) |
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Multiply both sides of equation (2) by 1133 Divide the two sides of equation (2) by 2323, the equation can be obtained: | - | 1133 3870 | B | | - | 26059 390870 | C | | - | 26059 390870 | D | = | | | 291181 2996670 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | | 387 100 | A | + | | | 67 25 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (1) |
| - | 2323 3870 | B | | - | 529 3870 | C | | - | 529 3870 | D | = | | | 257 1290 | | (2) |
| | | 60 101 | C | + | | | 60 101 | D | = | | | 57 2323 | | (3) |
| | | 119 1290 | B | + | | | 257 1290 | C | + | | | 257 1290 | D | = | | | 119 430 | | (4) |
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Multiply both sides of equation (2) by 357 Divide the two sides of equation (2) by 2323, the equation can be obtained: | - | 119 1290 | B | | - | 2737 130290 | C | | - | 2737 130290 | D | = | | | 30583 998890 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | | 387 100 | A | + | | | 67 25 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (1) |
| - | 2323 3870 | B | | - | 529 3870 | C | | - | 529 3870 | D | = | | | 257 1290 | | (2) |
| | | 60 101 | C | + | | | 60 101 | D | = | | | 57 2323 | | (3) |
| | | 774 4343 | C | + | | | 774 4343 | D | = | | | 714 2323 | | (4) |
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Multiply both sides of equation (3) by 13029 Divide the two sides of equation (3) by 43430, the equation can be obtained: | | | 1818 10201 | C | + | | | 1818 10201 | D | = | | | 171 23230 | (10) | , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | 387 100 | A | + | | | 67 25 | B | + | | | 13 10 | C | + | | | 13 10 | D | = | | | 3 10 | | (1) |
| - | 2323 3870 | B | | - | 529 3870 | C | | - | 529 3870 | D | = | | | 257 1290 | | (2) |
| | | 60 101 | C | + | | | 60 101 | D | = | | | 57 2323 | | (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》 |