detailed information: The input equation set is:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| | | 54 5 | A | + | | | 83 10 | B | + | | D | = | | | 44393 10 | | (2) |
| | | 23 10 | A | + | | | 53 10 | B | + | | | 133 10 | C | | -1 | D | = | | | 53853 10 | | (3) |
| | | 23 10 | B | + | | | 103 10 | C | | -1 | D | = | | | 34203 10 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 54 Divide the two sides of equation (1) by 5, the equation can be obtained: | | | 54 5 | A | + | | | 54 5 | B | + | | | 54 5 | C | = | | | 3930039 500 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | | - | 54 5 | C | + | | D | = | | - | 1710389 500 | | (2) |
| | | 23 10 | A | + | | | 53 10 | B | + | | | 133 10 | C | | -1 | D | = | | | 53853 10 | | (3) |
| | | 23 10 | B | + | | | 103 10 | C | | -1 | D | = | | | 34203 10 | | (4) |
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Multiply both sides of equation (1) by 23 Divide the two sides of equation (1) by 10, the equation can be obtained: | | | 23 10 | A | + | | | 23 10 | B | + | | | 23 10 | C | = | | | 3347811 2000 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | | - | 54 5 | C | + | | D | = | | - | 1710389 500 | | (2) |
| | 3 | B | + | | 11 | C | | -1 | D | = | | | 7422789 2000 | | (3) |
| | | 23 10 | B | + | | | 103 10 | C | | -1 | D | = | | | 34203 10 | | (4) |
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Multiply both sides of equation (2) by 6 Divide the two sides of equation (2) by 5, the equation can be obtained: | -3 | B | | - | 324 25 | C | + | | | 6 5 | D | = | | - | 5131167 1250 | (7) | , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | | - | 54 5 | C | + | | D | = | | - | 1710389 500 | | (2) |
| - | 49 25 | C | + | | | 1 5 | D | = | | - | 3935391 10000 | | (3) |
| | | 23 10 | B | + | | | 103 10 | C | | -1 | D | = | | | 34203 10 | | (4) |
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Multiply both sides of equation (2) by 23 Divide the two sides of equation (2) by 25, the equation can be obtained: | - | 23 10 | B | | - | 1242 125 | C | + | | | 23 25 | D | = | | - | 39338947 12500 | (8) | , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | | - | 54 5 | C | + | | D | = | | - | 1710389 500 | | (2) |
| - | 49 25 | C | + | | | 1 5 | D | = | | - | 3935391 10000 | | (3) |
| | | 91 250 | C | | - | 2 25 | D | = | | | 3414803 12500 | | (4) |
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Multiply both sides of equation (3) by 13 Divide the two sides of equation (3) by 70, the equation can be obtained: | - | 91 250 | C | + | | | 13 350 | D | = | | - | 51160083 700000 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | | - | 54 5 | C | + | | D | = | | - | 1710389 500 | | (2) |
| - | 49 25 | C | + | | | 1 5 | D | = | | - | 3935391 10000 | | (3) |
| - | 3 70 | D | = | | | 28013777 140000 | | (4) |
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Multiply both sides of equation (4) by 14 Divide both sides of equation (4) by 3, get the equation: | - | 1 5 | D | = | | | 28013777 30000 | (10) | , then add the two sides of equation (10) to both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | | - | 54 5 | C | + | | D | = | | - | 1710389 500 | | (2) |
| - | 49 25 | C | = | | | 4051901 7500 | | (3) |
| - | 3 70 | D | = | | | 28013777 140000 | | (4) |
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Multiply both sides of equation (4) by 70 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | | - | 54 5 | C | = | | | 7489109 6000 | | (2) |
| - | 49 25 | C | = | | | 4051901 7500 | | (3) |
| - | 3 70 | D | = | | | 28013777 140000 | | (4) |
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Multiply both sides of equation (3) by 270 Divide both sides of equation (3) by 49, get the equation: | - | 54 5 | C | = | | | 5209587 1750 | (12) | , then subtract both sides of equation (12) from both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | = | | | 145557 200 | | (1) |
| - | 5 2 | B | = | | - | 2904253 1680 | | (2) |
| - | 49 25 | C | = | | | 4051901 7500 | | (3) |
| |
Multiply both sides of equation (3) by 25 Divide both sides of equation (3) by 49, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
| | | | - | 5 2 | B | = | | - | 2904253 1680 | | (2) |
| - | 49 25 | C | = | | | 4051901 7500 | | (3) |
| |
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 5, get the equation:, then add the two sides of equation (14) to both sides of equation (1), get the equation:
| | | | - | 5 2 | B | = | | - | 2904253 1680 | | (2) |
| | |
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》 |