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About Systems of Equations — Class 8 IB

Solve systems of two linear equations graphically and algebraically. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 4). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Systems of Equations — solved examples for Class 8 IB

Example 1easy

Solve: \(x + y = 5\) and \(x = 3\). Find \(y\).
  1. A)1
  2. B)2
  3. C)3
  4. D)8

Step-by-step solution

  1. Substitute x = 3.
    3+y=5⇒y=23 + y = 5 \Rightarrow y = 2

Answer: 2

Example 2medium

Solve by substitution: \(y = 2x - 1\) and \(3x + y = 9\).
  1. A)x = 2, y = 3
  2. B)x = 1, y = 1
  3. C)x = 3, y = 5
  4. D)x = 2, y = 5

Step-by-step solution

  1. Substitute.
    3x+(2x−1)=9⇒5x=10⇒x=23x + (2x - 1) = 9 \Rightarrow 5x = 10 \Rightarrow x = 2
  2. Then \(y = 2(2) - 1 = 3\).

Answer: x = 2, y = 3

Example 3hard

Solve: \(3x + 4y = 18\) and \(5x - 2y = 4\).
  1. A)x = 2, y = 3
  2. B)x = 3, y = 2
  3. C)x = 4, y = 1.5
  4. D)x = 1, y = 3.75

Step-by-step solution

  1. Multiply second by 2: \(10x - 4y = 8\).
    3x+4y+10x−4y=18+8⇒13x=26⇒x=2,  y=33x + 4y + 10x - 4y = 18 + 8 \Rightarrow 13x = 26 \Rightarrow x = 2, \; y = 3

Answer: x = 2, y = 3

Practice questions on Systems of Equations

  1. Q1.easy

    Solve: \(x + y = 10\) and \(x - y = 2\). Find \(x\).
    1. A)4
    2. B)5
    3. C)6
    4. D)8
    Show answer

    Answer: 6

    Hint: Add the two equations to eliminate y.

  2. Q2.easy

    If \(x = 2\) and \(x + y = 7\), what is \(y\)?
    1. A)3
    2. B)4
    3. C)5
    4. D)9
    Show answer

    Answer: 5

    Hint: Substitute x = 2 into the second equation.

  3. Q3.easy

    Solve: \(2x + y = 8\) and \(y = 2\). Find \(x\).
    1. A)2
    2. B)3
    3. C)4
    4. D)5
    Show answer

    Answer: 3

    Hint: Substitute y = 2 into the first equation.

  4. Q4.medium

    Solve by elimination: \(2x + 3y = 12\) and \(2x + y = 8\).
    1. A)x = 3, y = 2
    2. B)x = 2, y = 3
    3. C)x = 4, y = 0
    4. D)x = 1, y = 6
    Show answer

    Answer: x = 3, y = 2

    Hint: Subtract the second equation from the first to eliminate x.

  5. Q5.medium

    Solve: \(x + y = 10\) and \(2x - y = 5\). Find \(x\) and \(y\).
    1. A)x = 5, y = 5
    2. B)x = 3, y = 7
    3. C)x = 7, y = 3
    4. D)x = 4, y = 6
    Show answer

    Answer: x = 5, y = 5

    Hint: Add the equations to eliminate y.

  6. Q6.medium

    Solve: \(3x + 2y = 16\) and \(x - 2y = 0\).
    1. A)x = 4, y = 2
    2. B)x = 2, y = 5
    3. C)x = 6, y = -1
    4. D)x = 8, y = -4
    Show answer

    Answer: x = 4, y = 2

    Hint: Add the equations to eliminate y.

  7. Q7.hard

    Solve: \(2x + 3y = 1\) and \(5x + 7y = 3\).
    1. A)x = -2, y = \frac{5}{3}
    2. B)x = 2, y = -1
    3. C)x = -2, y = 1
    4. D)x = 1, y = -\frac{1}{3}
    Show answer

    Answer: x = 2, y = -1

    Hint: Multiply to eliminate one variable.

  8. Q8.hard

    A cinema sells 200 tickets. Adult tickets cost 12andchildticketscost12 and child tickets cost 7. Total revenue is $1,900. How many adult tickets were sold?
    1. A)100
    2. B)110
    3. C)120
    4. D)130
    Show answer

    Answer: 120

    Hint: Set up: a + c = 200 and 12a + 7c = 1900.

  9. Q9.hard

    Solve: \(\frac{x}{2} + \frac{y}{3} = 4\) and \(\frac{x}{4} + \frac{y}{2} = 3\).
    1. A)x = 6, y = 3
    2. B)x = 4, y = 6
    3. C)x = 2, y = 4
    4. D)x = 6, y = 2
    Show answer

    Answer: x = 6, y = 3

    Hint: Multiply each equation by the LCD to clear fractions.

These are 9 of the 60 questions available for Systems of Equations. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.