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Free Digital SAT System of Equations Practice Questions with Video Explanations

System of equations questions ask students to solve for a variable in a system of two equations with two variables or to identify an equation(s) that represents a mathematical relationship in a text. System of equations questions appear on approximately 8.1% of the Digital SAT. System of equations questions fall under Algebra according to the College Board. Try our sample of 3 practice questions with video explanations.
 
1.
y=x+6,
2x+y=18
​
The solution to the given system of equations is (x,y). What is the value of x?

Question 1 of 3

2. At a school play, adult tickets cost $16 each and student tickets cost $10 each. A total of 160 adult and student tickets were sold, and the total revenue from ticket sales was $1,990.

How many student tickets were sold?

Question 2 of 3

3. y=x^2-8x+a,
y=4x-20

In the given system of equations, a is a constant. If the system has exactly one solution, what is the value of a?

Question 3 of 3


 

Related Topics

Solving for a Variable in Terms of Another

Systems of equations often require students to solve for one variable in terms of another. For example, a student may need to rearrange one equation to solve for y in terms of x before substituting that expression into the other equation. This is especially helpful when the system is not already written in a convenient form. Therefore, practicing solving for a variable in terms of another can help students answer systems of equations questions more efficiently.

Evaluating Functions

Systems of equations questions can involve evaluating functions. For example, students may need to determine whether a given point satisfies both equations by substituting the x-value into each function and checking the corresponding y-value. Evaluating functions can also help students compare two equations and identify their point of intersection. Therefore, practicing evaluating functions can help students better understand how to solve systems of equations. Go back to all of our free SAT math practice here.
Glyn Caddell - Founder of Caddell Prep

Glyn Caddell

Glyn Caddell holds a BS in Mechanical Engineering from NJIT and has been tutoring New York City students since 2008. He founded Caddell Prep in 2012 and is the author of Digital SAT Math Secrets: Lessons & Tricks to Quickly Improve to a Perfect 800 on the Math Test, which contains over 900 practice problems and is used in Caddell Prep’s SAT math classes. He is founding president of the Staten Island Technical High School alumni association and teaches every lesson on this site personally.