Worksheet: Solving Systems of Linear Equations Using Elimination

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In this worksheet, we will practice solving systems of linear equations using elimination.

Q1:

Use the elimination method to solve the simultaneous equations 𝑥−2𝑦=−2,2𝑥+3𝑦=10.

  • A 𝑥 = 1 and 𝑦=−1
  • B 𝑥 = − 1 6 and 𝑦=−14
  • C 𝑥 = 1 and 𝑦=1
  • D 𝑥 = − 1 4 and 𝑦=−16
  • E 𝑥 = 2 and 𝑦=2

Q2:

Use the elimination method to solve the simultaneous equations 5𝑥+𝑦=20,4𝑥+5𝑦=37.

  • A 𝑥 = 2 and 𝑦=6
  • B 𝑥 = 6 and 𝑦=8
  • C 𝑥 = 3 and 𝑦=5
  • D 𝑥 = 2 and 𝑦=10
  • E 𝑥 = 3 and 𝑦=25

Q3:

Using elimination, solve the simultaneous equations 3𝑥+7𝑦=34,9𝑥+10𝑦=91.

  • A 𝑥 = 9 , 𝑦 = − 1
  • B 𝑥 = 9 , 𝑦 = 1
  • C 𝑥 = 1 9 , 𝑦 = 1 1
  • D 𝑥 = 1 7 , 𝑦 = 1
  • E 𝑥 = 1 7 , 𝑦 = 4

Q4:

Using elimination, solve the simultaneous equations −5𝑥+7𝑦=9,15𝑥+12𝑦=39.

  • A 𝑥 = 2 , 𝑦 = 2
  • B 𝑥 = 2 , 𝑦 = 1
  • C 𝑥 = 2 , 𝑦 = 4
  • D 𝑥 = 1 , 𝑦 = − 2
  • E 𝑥 = 1 , 𝑦 = 2

Q5:

By first multiplying the equations to make the coefficients of either 𝑥 or 𝑦 equal, use the elimination method to solve the simultaneous equations 2𝑥+3𝑦=4,3𝑥+4𝑦=8. to find 𝑥 and 𝑦.

  • A 𝑥 = 3 and 𝑦=4
  • B 𝑥 = 2 and 𝑦=2
  • C 𝑥 = 8 and 𝑦=−4
  • D 𝑥 = − 4 and 𝑦=4
  • E 𝑥 = 4 and 𝑦=3

Q6:

Use the elimination method to solve the given simultaneous equations. −3𝑥+4𝑦=6−2𝑥−3𝑦=−13

  • A 𝑥 = 4 and 𝑦=6
  • B 𝑥 = 3 and 𝑦=11
  • C 𝑥 = 3 and 𝑦=2
  • D 𝑥 = 1 1 and 𝑦=3
  • E 𝑥 = 2 and 𝑦=3

Q7:

Use the elimination method to solve the simultaneous equations 4𝑥−2𝑦=4,5𝑥+3𝑦=16.

  • A 𝑥 = 1 2 and 𝑦=22
  • B 𝑥 = 3 and 𝑦=4
  • C 𝑥 = 2 and 𝑦=2
  • D 𝑥 = 4 and 𝑦=4
  • E 𝑥 = 1 0 and 𝑦=18

Q8:

Using elimination, solve the simultaneous equations 4𝑥+6𝑦=40,3𝑥+7𝑦=40.

  • A 𝑥 = 2 , 𝑦 = 4
  • B 𝑥 = 4 , 𝑦 = − 8
  • C 𝑥 = 8 , 𝑦 = 1 2
  • D 𝑥 = 4 , 𝑦 = 4
  • E 𝑥 = 1 , 𝑦 = 6

Q9:

Using elimination, solve the simultaneous equations 4𝑥+6𝑦=20,3𝑥−4𝑦=−2.

  • A 𝑥 = 4 , 𝑦 = 2
  • B 𝑥 = 2 , 𝑦 = 2
  • C 𝑥 = 2 , 𝑦 = − 4
  • D 𝑥 = 9 , 𝑦 = 9
  • E 𝑥 = 4 , 𝑦 = 6

Q10:

Using elimination, solve the simultaneous equations 5𝑥+4𝑦=27,3𝑥+12𝑦=45.

  • A 𝑥 = 1 , 𝑦 = 3
  • B 𝑥 = 3 , 𝑦 = 3
  • C 𝑥 = 3 , 𝑦 = 1
  • D 𝑥 = 5 , 𝑦 = 5
  • E 𝑥 = 7 , 𝑦 = 2

Q11:

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

  • A 𝑥 = 4 and 𝑦=6
  • B 𝑥 = 5 and 𝑦=4
  • C 𝑥 = 6 and 𝑦=4
  • D 𝑥 = 5 and 𝑦=3
  • E 𝑥 = 4 and 𝑦=5

Q12:

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

  • A 𝑥 = 1 and 𝑦=3
  • B 𝑥 = 6 and 𝑦=2
  • C 𝑥 = 2 and 𝑦=6
  • D 𝑥 = 1 2 and 𝑦=18
  • E 𝑥 = 3 and 𝑦=1

Q13:

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

  • A 𝑥 = 1 , 𝑦 = 3
  • B 𝑥 = 4 , 𝑦 = 2
  • C 𝑥 = 1 , 𝑦 = 2
  • D 𝑥 = 4 , 𝑦 = 1
  • E 𝑥 = − 1 , 𝑦 = 3

Q14:

Using elimination, solve the simultaneous equations 4𝑥+4𝑦=12,3𝑥+4𝑦=10.

  • A 𝑥 = 2 , 𝑦 = 1
  • B 𝑥 = − 2 , 𝑦 = 1
  • C 𝑥 = 2 , 𝑦 = − 1
  • D 𝑥 = 1 , 𝑦 = 2
  • E 𝑥 = 5 , 𝑦 = − 2

Q15:

Using elimination, solve the simultaneous equations 3𝑥+2𝑦=14,6𝑥−2𝑦=22.

  • A 𝑥 = 2 , 𝑦 = 1
  • B 𝑥 = − 4 , 𝑦 = − 1
  • C 𝑥 = 1 2 , 𝑦 = − 2 5
  • D 𝑥 = 4 , 𝑦 = 2
  • E 𝑥 = 4 , 𝑦 = 1

Q16:

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

  • A 𝑥 = 1 , 𝑦 = 1
  • B 𝑥 = 4 , 𝑦 = 5
  • C 𝑥 = 1 , 𝑦 = 2
  • D 𝑥 = 2 , 𝑦 = 2
  • E 𝑥 = 2 , 𝑦 = 1

Q17:

Use the elimination method to solve the simultaneous equations 23𝑥+34𝑦=1724,43𝑥+53𝑦=32.

  • A 𝑥 = 1 5 3 2 and 𝑦=112
  • B 𝑥 = 1 2 and 𝑦=12
  • C 𝑥 = 1 5 8 and 𝑦=12
  • D 𝑥 = 2 and 𝑦=2
  • E 𝑥 = 1 7 and 𝑦=112

Q18:

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

  • A 𝑎 = 4 and 𝑏=1
  • B 𝑎 = 2 and 𝑏=8
  • C 𝑎 = 2 and 𝑏=4
  • D 𝑎 = 3 and 𝑏=2
  • E 𝑎 = 1 0 and 𝑏=2

Q19:

Using elimination, solve the simultaneous equations 5𝑥−4𝑦=21,4𝑥+12𝑦=32.

  • A 𝑥 = 5 , 𝑦 = 4
  • B 𝑥 = 4 , 𝑦 = 5
  • C 𝑥 = 4 , 𝑦 = 1
  • D 𝑥 = 1 , 𝑦 = 5
  • E 𝑥 = 5 , 𝑦 = 1

Q20:

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

  • A 𝑥 = 0 and 𝑦=6
  • B 𝑥 = − 4 and 𝑦=12
  • C 𝑥 = 2 and 𝑦=5
  • D 𝑥 = − 1 6 and 𝑦=30
  • E 𝑥 = 2 and 𝑦=3

Q21:

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

  • A 𝑎 = 3 and 𝑏=5
  • B 𝑎 = 6 and 𝑏=−1
  • C 𝑎 = 6 and 𝑏=2
  • D 𝑎 = 3 and 𝑏=−1
  • E 𝑎 = 2 and 𝑏=2

Q22:

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

  • A 𝑎 = 4 and 𝑏=2
  • B 𝑎 = 2 and 𝑏=2
  • C 𝑎 = 1 2 and 𝑏=8
  • D 𝑎 = 1 2 and 𝑏=10
  • E 𝑎 = 4 and 𝑏=4

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