Systems of Linear Equations Practice Tests

These Grade 8 Math practice tests cover graphing systems, intersections, substitution, elimination, equivalent systems, one solution, no solution, infinite solutions, and real-world models.

Skills covered

  • Solving systems by graphing, substitution, and elimination
  • Interpreting an ordered-pair intersection as the solution to both equations
  • Identifying parallel lines, the same line, one solution, no solution, and infinitely many solutions
  • Checking ordered pairs in both original equations
  • Modeling ticket sales, mixtures, rates, dimensions, coins, plans, and number relationships

How to use these practice tests

Choose a method that fits the system. After finding an ordered pair, substitute it into both equations and verify that the context makes sense.

For more Grade 8 Math practice, return to the Grade 8 Math category.

3. Test

Grade 8 Systems of Linear Equations Practice Tests

Practice Grade 8 Math questions about systems of linear equations, graphing, substitution, elimination, intersections, no solutions, infinite solutions, and applications.

Choose the best answer for each question. Check the ordered pair in both original equations and review the explanation after submitting your answers.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Solve by elimination: x+y=9x+y=9 and x−y=1x-y=1.

Please select an answer first.

Correct answer: A

The correct answer is (x,y)=(5,4)(x,y)=(5,4).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add the equations: 2x=102x=10, so x=5x=5. Then y=4y=4.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add the equations: 2x=102x=10, so x=5x=5. Then y=4y=4.

2. QuestionMultiple choice

Solve by elimination: 2x+3y=122x+3y=12 and 2x−y=42x-y=4.

Please select an answer first.

Correct answer: B

The correct answer is (x,y)=(3,2)(x,y)=(3,2).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Subtract the second equation from the first: 4y=84y=8, so y=2y=2. Then x=3x=3.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Subtract the second equation from the first: 4y=84y=8, so y=2y=2. Then x=3x=3.

3. QuestionMultiple choice

Solve by elimination: 3x+2y=163x+2y=16 and 3x−2y=83x-2y=8.

Please select an answer first.

Correct answer: C

The correct answer is (x,y)=(4,2)(x,y)=(4,2).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add the equations: 6x=246x=24, so x=4x=4. Substitution gives y=2y=2.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add the equations: 6x=246x=24, so x=4x=4. Substitution gives y=2y=2.

4. QuestionMultiple choice

Solve by elimination: 4x+y=134x+y=13 and 2x−y=52x-y=5.

Please select an answer first.

Correct answer: D

The correct answer is (x,y)=(3,1)(x,y)=(3,1).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add the equations: 6x=186x=18, so x=3x=3. Then y=1y=1.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add the equations: 6x=186x=18, so x=3x=3. Then y=1y=1.

5. QuestionMultiple choice

Solve by elimination: 5x+2y=245x+2y=24 and 5x−2y=165x-2y=16.

Please select an answer first.

Correct answer: A

The correct answer is (x,y)=(4,2)(x,y)=(4,2).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add to get 10x=4010x=40, so x=4x=4. Then y=2y=2.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add to get 10x=4010x=40, so x=4x=4. Then y=2y=2.

6. QuestionMultiple choice

Solve the system x+2y=7x+2y=7 and 3x−2y=93x-2y=9.

Please select an answer first.

Correct answer: B

The correct answer is (x,y)=(4,frac32)(x,y)=(4,\\frac{3}{2}).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add the equations: 4x=164x=16, so x=4x=4. Then 4+2y=74+2y=7, giving y=frac32y=\\frac{3}{2}.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add the equations: 4x=164x=16, so x=4x=4. Then 4+2y=74+2y=7, giving y=frac32y=\\frac{3}{2}.

7. QuestionMultiple choice

Solve by elimination: 2x+y=82x+y=8 and 4x−y=104x-y=10.

Please select an answer first.

Correct answer: C

The correct answer is (x,y)=(3,2)(x,y)=(3,2).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add the equations: 6x=186x=18, so x=3x=3. Then y=2y=2.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add the equations: 6x=186x=18, so x=3x=3. Then y=2y=2.

8. QuestionMultiple choice

Solve by elimination: 3x+4y=183x+4y=18 and 3x−4y=23x-4y=2.

Please select an answer first.

Correct answer: D

The correct answer is (x,y)=(frac103,2)(x,y)=(\\frac{10}{3},2).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add the equations: 6x=206x=20, so x=frac103x=\\frac{10}{3}. Substitution gives y=2y=2.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add the equations: 6x=206x=20, so x=frac103x=\\frac{10}{3}. Substitution gives y=2y=2.

9. QuestionMultiple choice

Solve the system 2x+5y=192x+5y=19 and 2x−5y=12x-5y=1.

Please select an answer first.

Correct answer: A

The correct answer is (x,y)=(5,frac95)(x,y)=(5,\\frac{9}{5}).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add to get 4x=204x=20, so x=5x=5. From the first equation, 10+5y=1910+5y=19, so y=frac95y=\\frac{9}{5}.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add to get 4x=204x=20, so x=5x=5. From the first equation, 10+5y=1910+5y=19, so y=frac95y=\\frac{9}{5}.

10. QuestionMultiple choice

Solve by elimination: 7x+2y=207x+2y=20 and 7x−2y=87x-2y=8.

Please select an answer first.

Correct answer: B

The correct answer is (x,y)=(2,3)(x,y)=(2,3).

  1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
  2. Solve for the ordered pair: Add the equations: 14x=2814x=28, so x=2x=2. Then 14+2y=2014+2y=20, giving y=3y=3.
  3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Add the equations: 14x=2814x=28, so x=2x=2. Then 14+2y=2014+2y=20, giving y=3y=3.