Open Practice Tests

Systems of linear equations — Topic practice

5 exercises · 4 automatically checked · 1 written self-check · Untimed

Instructions and review guidance

4 questions · Shuffled order · Untimed practice

Work through the set before checking solutions. Guide question labels match the source lesson references. 1 written response appears below the question bank, with model answers for self-review; these are not automatically graded.

Guide question labels stay the same when the order changes. Check answers when you are ready to review.

Written self-checks are below the question bank and are excluded from the automatic score.

Written responses are self-review exercises.

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The drill

Question 2

  • Guide question E4B

How many solutions satisfy 2x + 3y = 12 and 4x + 6y = 20?

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Question 3

  • Guide question E4C

If x + 2y = 9 and 3x − y = 6, find x + y.

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Question 4

  • Guide question E4D

For which k do 2x + y = 4 and kx + 3y = 12 have infinitely many solutions?

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Question 5

  • Guide question E4E

If 3x + 2y = 17 and x + 4y = 9, find 4x + 6y.

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

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Written self-checks

Write your complete response before opening the model answer. Compare both your answer and your reasoning.

Guide question E4A

Solve x + y = 9 and x − y = 1.

Show model answerHide model answer for question E4A

(5, 4). Adding the equations gives 2x = 10, so x = 5. Then y = 9 − 5 = 4. Both 5 + 4 = 9 and 5 − 4 = 1 hold.