Linear Combination

Alright! Here it is our first linear equation! We must solve this equation in order for us to get off the yellow brick road and into the forest! The problem is 2x - 4y= 13 and 4x - 5y= 8. To help us with the math is my dear friend the Scarecrow who recently recieved a diploma!

Your first step when performing linear combination is to multiply one or both of the equations by a constant so that you only differ in one of the variables. In this problem you will multiply the first equation by -2 to get a -4x in the first equation.

2x - 4y= 13 (multiply -2)

-4x + 8y= -26

Add the revised equations from the first step to the second original equation. Combining like terms will eliminate at least one of the variables. Then solve for the rest of the variables.

3y= -18

y= -6

Finaly, subsitute the value you got from step 2 into either one of the original problems and solve for your remaining variable.

2x - 4y= 13

2x -4(-6)= 13

2x + 24= 13

x= -11/2

Your final solution should be ( -11/2, -6)! AAlso, you can check your answer by using a graphing calculator.