McGraw-Hill Education GRE 2019

Let’s look at another example:

If √x + 2 − 3 = 4, what is the value of x?

SOLUTION:

Step 1: Isolate √x + 2 by adding 3 to both sides of the equation.

√x + 2 − 3 = 4

+ 3 = + 3

√x + 2 = 7

Step 2: (x + 2) is within parentheses, so you should manipulate the equation

to isolate the expression within the parentheses. To do so, square both sides

of the equation.

√x + 2 = 7

(^) √x + 2 2 = 7 2
x + 2 = 49
Systems of Equations: Combination and Substitution
Often, the GRE will present you with two or more equations with multiple
variables and will ask you to solve for the value of one or more of the variables in
those equations. This is called a system of equations. When working with a system
of equations, your ultimate goal is to arrive at a situation similar to what you saw
in the previous section: one equation with one variable. To accomplish this, you can
take two approaches: substitution or combination.
Substitution
Let’s say you are given the following question:
3 x + 2y = 18
2 x + y = 9
What is x?
Step 1: Express one variable in terms of the other variable.
3 x + 2y = 18
y = 9 − 2x
Step 2: Take the expression for y and substitute it for y in the first equation:
3 x + 2(9 − 2x) = 18.
CHAPTER 11 ■ ALGEBRA 261
03-GRE-Test-2018_173-312.indd 261 12/05/17 11:53 am