Systems of Linear Equations Quiz

Grade 8 · Math · Quiz

Test your ability to solve and interpret systems of linear equations.

Questions

1. Solve: y = x + 2 and y = 3x - 4. What is the solution?

   1. (3, 5)
   2. (2, 4)
   3. (1, 3)
   4. (4, 6)
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   Answer: (3, 5)

   Set x+2=3x-4 → -2x=-6 → x=3; y=3+2=5.

2. The elimination method always requires multiplying one or both equations before adding.

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   Answer: False

   If coefficients already match (or cancel by adding), no multiplication is needed.

3. Which ordered pair satisfies both: 2x + y = 5 and x - y = 1?

   1. (1, 3)
   2. (2, 1)
   3. (3, -1)
   4. (0, 5)
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   Answer: (2, 1)

   Add equations: 3x=6 → x=2; y=2-1=1. Check: 2(2)+1=5 ✓, 2-1=1 ✓.

4. Two equations that represent the same line have ___ many solutions.

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   Answer: infinitely

   Identical lines share every point, producing infinitely many solutions.

5. What is the y-value in the solution to: x + 2y = 8 and x - y = 2?

   1. 1
   2. 2
   3. 3
   4. 4
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   Answer: 2

   Subtract: (x+2y)-(x-y)=8-2 → 3y=6 → y=2.

6. If two linear equations have the same slope and the same y-intercept, the system has no solution.

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   Answer: False

   Same slope AND same y-intercept means the lines are identical — infinitely many solutions, not zero.

7. A system has equations y = 2x + 3 and y = 2x - 5. How many solutions does it have?

   1. One
   2. Two
   3. Infinitely many
   4. None
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   Answer: None

   Same slope (2), different y-intercepts (3 vs -5) means parallel lines — no intersection.

8. In the substitution method, you first ___ one variable in terms of the other.

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   Answer: isolate

   Substitution requires expressing one variable as a function of the other before substituting.

9. Solve by substitution: y = 3x and 2x + y = 10. What is x?

   1. 1
   2. 2
   3. 3
   4. 4
   Show answer

   Answer: 2

   Substitute y=3x into 2x+3x=10 → 5x=10 → x=2.

10. The graphing method gives the most precise solution when the intersection is not at integer coordinates.

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    Answer: False

    Graphing is least precise when the answer is not integer-valued; algebraic methods are more accurate.

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