GED Math: Systems of Equations Practice Test

15 Systems of Equations Practice Questions

This free GED Math practice test contains 15 systems of equations questions ranging from easy to hard. The quiz covers solving linear systems, word problems, and applications of systems of equations. Complete the test to receive instant feedback and explanations for each question.

Perfect for GED test preparation and assessing your readiness for the algebra section of the GED exam.

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0/15 answered
1. Solve the system: Easy
\( x + y = 10 \)
\( x - y = 2 \)
What is the value of \(x\) and \(y\)?
2. Solve the system: Easy
\( 3x + 4y = 12 \)
\( 2x - y = 4 \)
What is the value of \(x\) and \(y\)?
3. Solve the system: Easy
\( 2x + 3y = 13 \)
\( x - y = 1 \)
What is the value of \(x\) and \(y\)?
4. Solve the system: Easy
\( 4x + y = 7 \)
\( 3x - y = 8 \)
What is the value of \(x\) and \(y\)?
5. Solve the system: Easy
\( x + 2y = 6 \)
\( 3x - y = 7 \)
What is the value of \(x\) and \(y\)?
6. Solve the system: Medium
\( 2x - y = 3 \)
\( 5x + 3y = 19 \)
What is the value of \(x\) and \(y\)?
7. Solve the system: Medium
\( 3x + 2y = 10 \)
\( x - y = 4 \)
What is the value of \(x\) and \(y\)?
8. Solve the system: Medium
\( 4x + y = 11 \)
\( 2x + 3y = 16 \)
What is the value of \(x\) and \(y\)?
9. Solve the system: Medium
\( 5x + 2y = 12 \)
\( 3x + y = 7 \)
What is the value of \(x\) and \(y\)?
10. Word problem: Medium
A farmer has 50 chickens and ducks in total. The total number of legs of the chickens and ducks is 140.

\( x + y = 50 \)
\( 2x + 4y = 140 \)
How many chickens and how many ducks are there?
11. Word problem: Hard
Two numbers have a sum of 18. The difference between the two numbers is 6.

\( x + y = 18 \)
\( x - y = 6 \)
What are the two numbers?
12. Solve the system: Hard
\( 3x - 2y = 7 \)
\( 5x + 4y = 23 \)
What is the value of \(x\) and \(y\)?
13. Word problem: Hard
A store sells pencils for $0.50 each and erasers for $1.20 each. A customer buys a total of 12 items and spends $9.60.

\( x + y = 12 \)
\( 0.5x + 1.2y = 9.6 \)
How many pencils and erasers did they buy?
14. Solve the system: Hard
\( 2x + 3y = 11 \)
\( 5x - 2y = 12 \)
What is the value of \(x\) and \(y\)?
15. Word problem: Hard
A group of students raised $360 for a charity. The group sold 3 tickets for every 2 sold by another group. If both groups together sold 120 tickets, how many tickets did each group sell?

\( x + y = 120 \)
\( 3x = 2y \)
What is the number of tickets sold by each group?

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