The third way to solve a sytem is by linear combination. |
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Solving by use of linear combination is practical when nether graphing nor substitution is an option. |
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| The first step is to multiply by the loewest number you can in order to get the same number only a different number. (4 and -4). | |
| The second step is to add the two equations together by combining like terms. This will elminate one of the variables. | |
| The third step is to solve for the remaing variable | |
| The fourth step is to Substitute the solution into either one of the original equations. | |
| The fifth step is to solve for the remaining value. |
Example1 |
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Solve the system using linear combination method. 2x-5y=10 -3x+4y=-15 |
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| Multiply by the lowest number you can to get a common number with a different sign | 3(2x-5y=10)=6x-15y=30 2(-3x+4y=-15)=-6x+8y=-30 |
| Add the two equations together | 6x-15y=30 -6x+8y=-30 -7y=0 |
| Solve for y | y=0 |
| Substitute the y in one of the original equations | 2x-5(0)=10
or -3x+4(0)=-15 |
| Solve for x | x=5 |
| Your answer is... | (5,0) |