Lesson Worksheet: Solving a System of Two Linear Equations by Elimination Using Addition and Subtraction Mathematics

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In this worksheet, we will practice solving systems of two linear equations by elimination using addition and subtraction.

Q1:

Use the elimination method to solve the simultaneous equations 3𝑎+4𝑏=14,−3𝑎+5𝑏=4.

  • A𝑎=3 and 𝑏=5
  • B𝑎=6 and 𝑏=−1
  • C𝑎=6 and 𝑏=2
  • D𝑎=3 and 𝑏=−1
  • E𝑎=2 and 𝑏=2

Q2:

Use the elimination method to solve the simultaneous equations 6𝑥−3𝑦=18,5𝑥+3𝑦=37.

  • A𝑥=4 and 𝑦=6
  • B𝑥=5 and 𝑦=4
  • C𝑥=6 and 𝑦=4
  • D𝑥=5 and 𝑦=3
  • E𝑥=4 and 𝑦=5

Q3:

Using elimination, solve the simultaneous equations 3𝑥+4𝑦=7,3𝑥+2𝑦=5.

  • A𝑥=1, 𝑦=1
  • B𝑥=4, 𝑦=5
  • C𝑥=1, 𝑦=2
  • D𝑥=2, 𝑦=2
  • E𝑥=2, 𝑦=1

Q4:

Use the elimination method to solve the simultaneous equations 3𝑎+2𝑏=14,4𝑎+2𝑏=16.

  • A𝑎=4 and 𝑏=1
  • B𝑎=2 and 𝑏=8
  • C𝑎=2 and 𝑏=4
  • D𝑎=3 and 𝑏=2
  • E𝑎=10 and 𝑏=2

Q5:

Using elimination, solve the simultaneous equations −5𝑥+6𝑦=13,5𝑥+2𝑦=11.

  • A𝑥=1, 𝑦=3
  • B𝑥=4, 𝑦=2
  • C𝑥=1, 𝑦=2
  • D𝑥=4, 𝑦=1
  • E𝑥=−1, 𝑦=3

Q6:

Solve the simultaneous equations 𝑥6+𝑦6=1 and 𝑥6+𝑦9=172.

  • A𝑥=147, 𝑦=141
  • B𝑥=141, 𝑦=147
  • C𝑥=141, 𝑦=−135
  • D𝑥=−135, 𝑦=141

Q7:

Solve the simultaneous equations 𝑥−𝑦=4 and 𝑥+𝑦=14.

  • A𝑥=9, 𝑦=5
  • B𝑥=5, 𝑦=9
  • C𝑥=23, 𝑦=9
  • D𝑥=9, 𝑦=23

Q8:

Use the elimination method to solve the simultaneous equations 3𝑥+4𝑦=18,3𝑥+2𝑦=12.

  • A𝑥=0 and 𝑦=6
  • B𝑥=−4 and 𝑦=12
  • C𝑥=2 and 𝑦=5
  • D𝑥=−16 and 𝑦=30
  • E𝑥=2 and 𝑦=3

Q9:

Use the elimination method to solve the simultaneous equations 6𝑥−4𝑦=14,4𝑥−4𝑦=8.

  • A𝑥=1 and 𝑦=3
  • B𝑥=6 and 𝑦=2
  • C𝑥=2 and 𝑦=6
  • D𝑥=12 and 𝑦=18
  • E𝑥=3 and 𝑦=1

Q10:

Use the elimination method to solve the simultaneous equations−3𝑎+4𝑏=4,−3𝑎+5𝑏=8.

  • A𝑎=4 and 𝑏=2
  • B𝑎=2 and 𝑏=2
  • C𝑎=12 and 𝑏=8
  • D𝑎=12 and 𝑏=10
  • E𝑎=4 and 𝑏=4

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