The Linear Combination Method

AKA

Elimination Method

Step 1) Multiply one or both of the equations by a constant to obtain coefficents 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 variable .

Solve the linear system using elimination

 2x - 4y = 13

4x - 5y = 8

 Equation 1

Equation 2

Solution
1) Multiply the first equation by -2 so that the x - coefficents 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
3)Substitute the value of y into the original equations .Solve for x. 2x - 4y =13

2x - 4 (-6) =13

2x + 24 = 13

x = - 11/2

 Write equation 1

Substitute -6 for y

Simplify

Solve for x
The solution is (-11/2, -6). Check you can check the solution algebraically using the method shown in Example1. You can also use a gaphing calculator to check the solution.

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