McGraw-Hill Education GRE 2019

Step 3: Solve for x.

3 x + 18 − 4x = 18

−x + 18 = 18

−x = 0

x = 0

Combination

Most systems of equations on the GRE can be solved with substitution, but you will

sometimes need to use combination. Let’s look at an example:

3 a + 2z = 12

4 a + 3z = 18

Solve for a and z.

Step 1: When solving by combination, your ultimate goal is to arrive at the

same coefficient for one of the variables. To do so, you will have to multiply

each equation by a factor that will yield you a common coefficient for one of

the variables. In this case, let’s make the coefficients on z equal to 6:

3(3a + 2z = 12) → 9 a + 6z = 36

2(4a + 3z = 18) → 8 a + 6z = 36

Step 2: Multiply across one equation by negative 1.

−1(9a + 6z = 36) = −9a − 6z = −36

8 a + 6z = 36

Step 3: Add the equations to arrive at one equation and one variable (your

ultimate goal!).

−9a − 6z = −36

8 a + 6z = 36

−a = 0

a = 0

Substitute 0 for a into either equation to solve for x:

3(0) + 2z = 12

2 z = 12

z = 6

262 PART 4 ■ MATH REVIEW

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