detailed information: The input equation set is:
| | | | | | | -30 | A | + | | 15 | B | | -10 | D | + | | 5 | E | = | | 0 | | (5) |
| Question solving process:
Add both sides of equation (1) to both sides of equation (2) ,the equations are reduced to:
| | | | | | | -30 | A | + | | 15 | B | | -10 | D | + | | 5 | E | = | | 0 | | (5) |
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Multiply both sides of equation (1) by 30, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (4), the equations are reduced to:
| | | | | | | -30 | A | + | | 15 | B | | -10 | D | + | | 5 | E | = | | 0 | | (5) |
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Multiply both sides of equation (1) by 30, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (5), the equations are reduced to:
Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
Multiply both sides of equation (2) by 45, the equation can be obtained: | | 45 | B | + | | 45 | C | + | | 45 | D | = | | 135 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 45, the equation can be obtained: | | 45 | B | + | | 45 | C | + | | 45 | D | = | | 135 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
交After the exchange of equation (3) and equation (4), the equation system becomes:
Multiply both sides of equation (3) by 9 Divide the two sides of equation (3) by 10, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (4) by 29 Divide the two sides of equation (4) by 2, the equation can be obtained: , then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (5) by 2 Divide both sides of equation (5) by 39, get the equation:, then subtract both sides of equation (12) from both sides of equation (4), get the equation:
Multiply both sides of equation (4) by 45, get the equation:, then add the two sides of equation (13) to both sides of equation (3), get the equation:
Subtract both sides of equation (4) from both sides of equation (2), get the equation:
Divide both sides of equation (3) by 50, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
Subtract both sides of equation (2) from both sides of equation (1), get the equation:
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》 |