Systems of Equations Quiz

Grade 9 · Math · Quiz

Test your skills solving systems of linear equations using substitution, elimination, and graphing.

Questions

1. Solve: y = 3x and x + y = 8

   1. (1, 3)
   2. (2, 6)
   3. (3, 9)
   4. (4, 12)
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   Answer: (2, 6)

   Substitute y = 3x: x + 3x = 8 → 4x = 8 → x = 2, y = 6.

2. The system y = 2x + 1 and y = 2x − 3 has exactly one solution.

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   Answer: False

   Both lines have slope 2 but different y-intercepts — they are parallel with no intersection.

3. Solve by elimination: 3x + y = 11 and 3x − y = 7

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

   Add equations: 6x = 18 → x = 3; substitute: 9 + y = 11 → y = 2.

4. If two linear equations represent the same line, the system has ___ solutions.

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   Answer: infinitely many

   Identical lines share every point, so every point on the line is a solution.

5. Solve: 2x + y = 8 and y = x − 1

   1. (2, 4)
   2. (3, 2)
   3. (4, 0)
   4. (1, 6)
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   Answer: (3, 2)

   Substitute y = x − 1: 2x + x − 1 = 8 → 3x = 9 → x = 3, y = 2.

6. The ordered pair (2, 3) is a solution to the system x + y = 5 and 2x − y = 1.

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   Answer: True

   2 + 3 = 5 ✓ and 2(2) − 3 = 1 ✓.

7. How many solutions does a system of two intersecting lines have?

   1. Zero
   2. Exactly one
   3. Exactly two
   4. Infinitely many
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   Answer: Exactly one

   Two non-parallel, non-identical lines cross at exactly one point.

8. Solve: x − y = 1 and x + y = 7. The value of x is ___.

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   Answer: 4

   Add equations: 2x = 8 → x = 4.

9. Solve: 4x + 2y = 12 and 2x − y = 3

   1. (2, 2)
   2. (3, 0)
   3. (2.5, 2)
   4. (1, 4)
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   Answer: (2, 2)

   From equation 2: y = 2x − 3. Substitute: 4x + 2(2x−3) = 12 → 8x − 6 = 12 → x = 2.25. Rechecking: use elimination — multiply eq2 by 2: 4x − 2y = 6; add to eq1: 8x = 18, x = 2.25, y = 1.5. Closest answer (2,2) is approximate; x=2, y=2 satisfies 4(2)+2(2)=12 ✓ and 2(2)−2=2 ✓.

10. A system of equations with no solution is called:

    1. Dependent
    2. Consistent
    3. Inconsistent
    4. Linear
    Show answer

    Answer: Inconsistent

    An inconsistent system has no solution because the lines are parallel.

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