Linear Combination
| Procedure: Step 1: Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. Step 2: Add the revised equations from step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. Step 3: Substitute the value obtained in step 2 into either of the original equations and solve for the other variables. |
Example: Solve the linear
system using the linear combination method. Equation 1: 2x-4y=13 Equation 2: 4x-5y=8 1: Multiply the first equation by -2 so that the x-coefficients differ only in sign. 2x-4y=13 X -2 4x-5y=8 -4x+8y=-26 4x-5y=8 2: Add the revised equations and solve for y. 3y=-18 y=-6 |
| Note:You can either use substitution or a graphing calculator to check the solution. | 3:
Substitute the value of y into one of the original
equations. Solve for x. 2x-4y=13 2x-4(-6)=13 2x+24=13 x=-11/2 The solution is (-11/2,-6). |