detailed information: The input equation set is:
 | | | | | | - | 1333 500 | A | + | | | 2983 50 | B | | - | 33 50 | C | + | | | 33 50 | D | = | | | 218 5 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 2, the equation can be obtained: , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 | | | | | | - | 1333 500 | A | + | | | 2983 50 | B | | - | 33 50 | C | + | | | 33 50 | D | = | | | 218 5 | | (4) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 | | | | | | - | 1333 500 | A | + | | | 2983 50 | B | | - | 33 50 | C | + | | | 33 50 | D | = | | | 218 5 | | (4) |
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Multiply both sides of equation (1) by 1333 Divide the two sides of equation (1) by 1200, the equation can be obtained: | | | 1333 500 | A | | - | 1333 240 | B | = | | | 1333 1200 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 | | | | | | | | 64927 1200 | B | | - | 33 50 | C | + | | | 33 50 | D | = | | | 53653 1200 | | (4) |
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Multiply both sides of equation (2) by 4 Divide the two sides of equation (2) by 5, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 | | | | | | | | 64927 1200 | B | | - | 33 50 | C | + | | | 33 50 | D | = | | | 53653 1200 | | (4) |
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Multiply both sides of equation (2) by 64927 Divide the two sides of equation (2) by 15000, the equation can be obtained: | - | 64927 1200 | B | + | | | 64927 2500 | C | = | | | 64927 6000 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 | | | | | | | | 63277 2500 | C | + | | | 33 50 | D | = | | | 13883 250 | | (4) |
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Multiply both sides of equation (3) by 63277 Divide the two sides of equation (3) by 12000, the equation can be obtained: | - | 63277 2500 | C | + | | | 63277 1000 | D | = | | 0 | (10) | , then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 | | | | | | | | 63937 1000 | D | = | | | 13883 250 | | (4) |
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Multiply both sides of equation (4) by 12000 Divide both sides of equation (4) by 63937, get the equation: | | | 45132 3761 | D | = | | | 666384 63937 | (11) | , then subtract both sides of equation (11) from both sides of equation (3), get the equation:
 | | | | | - | 24 5 | C | = | | - | 666384 63937 | | (3) |
| | | 63937 1000 | D | = | | | 13883 250 | | (4) |
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Multiply both sides of equation (3) by 5 Divide both sides of equation (3) by 4, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
 | | | | - | 25 2 | B | = | | - | 1346275 127874 | | (2) |
| - | 24 5 | C | = | | - | 666384 63937 | | (3) |
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Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 5, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
 | | | | - | 25 2 | B | = | | - | 1346275 127874 | | (2) |
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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》 |