# SAT Practice Questions: Solving Systems of Inequalities

If you encounter a question on the SAT Math exam that deals with systems of inequalities, you can solve it using the same approach as for a system of equations.

The following practice questions ask you to find the minimum and maximum possible values of a *y*-coordinate in a given solution set.

## Practice questions

**In the***xy*-plane, if a point with the coordinates (*c*,*d*) lies in the solution set of this system of inequalities, what is the minimum possible value of*d*?

*y*> –4*x*+ 540

*y*> 2*x*

**A.**Slightly below 90

**B.**Slightly above 90

**C.**Slightly below 180

**D.**Slightly above 180- In the
*xy*-plane, if a point with the coordinates (*e*,*f*) lies in the solution set of this system of inequalities, what is the maximum possible value of*f*?

*y*< –*x*+ 1,000

*y*< 2*x*+ 100

**A.**Slightly below 300

**B.**Slightly above 300

**C.**Slightly below 700

**D.**Slightly above 700

## Answers and explanations

**The correct answer is Choice (D).**

Combine the inequalities to find the (*x*,*y*) values of where the lines cross. First subtract the second inequality from the first inequality; then solve for*x*:

Now plug in 90 for*x*in the second inequality to solve for*y*:

The (*x*,*y*) values of where the lines cross are (90, 180).

Because each inequality has a*y*that’s*greater than*the expression with the*x*, anything*above*the lines is within the solution set;*d*represents the*y*-value of where the lines cross, so the answer is slightly above 180.**The correct answer is Choice (C).**

Combine the inequalities to find the (*x*,*y*) values of where the lines cross. First subtract the second inequality from the first inequality; then solve for*x*:

Now plug in 300 for*x*in the second inequality to solve for*y*:

The (*x*,*y*) values of where the lines cross are (300, 700).

Because each inequality has a*y*that’s*less than*the expression with the*x*, anything*below*the lines is within the solution set;*f*represents the*y*-value of where the lines cross, so the answer is slightly below 700.