Worksheet: Solving Systems of Linear Equations by Elimination

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

Q1:

Solve the simultaneous equations 𝑥 − 𝑦 = 8 and 3 𝑥 − 5 𝑦 + 1 0 = 0 .

  • A 𝑥 = 1 7 , 𝑦 = 2 5
  • B 𝑥 = − 9 , 𝑦 = 1 7
  • C 𝑥 = 2 5 , 𝑦 = − 1 7
  • D 𝑥 = 2 5 , 𝑦 = 1 7

Q2:

Use the elimination method to solve the simultaneous equations

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

Q3:

Use the elimination method to solve the simultaneous equations

  • A 𝑥 = 6 and 𝑦 = 8
  • B 𝑥 = 2 and 𝑦 = 1 0
  • C 𝑥 = 2 and 𝑦 = 6
  • D 𝑥 = 3 and 𝑦 = 5
  • E 𝑥 = 3 and 𝑦 = 2 5

Q4:

Solve the simultaneous equations 𝑥 + 𝑦 = 6 and 𝑦 − 1 9 = 0 .

  • A 𝑥 = 2 5 , 𝑦 = − 1 9
  • B 𝑥 = 1 3 , 𝑦 = − 1 9
  • C 𝑥 = − 1 9 , 𝑦 = 2 5
  • D 𝑥 = − 1 3 , 𝑦 = 1 9
  • E 𝑥 = 1 9 , 𝑦 = − 1 3

Q5:

Using elimination, solve the simultaneous equations

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

Q6:

Using elimination, solve the simultaneous equations

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

Q7:

By first multiplying the equations to make the coefficients of either 𝑥 or 𝑦 equal, use the elimination method to solve the simultaneous equations to find 𝑥 and 𝑦 .

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

Q8:

Use the elimination method to solve the given simultaneous equations.

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

Q9:

Use the elimination method to solve the simultaneous equations

  • A 𝑥 = 1 2 and 𝑦 = 2 2
  • B 𝑥 = 1 0 and 𝑦 = 1 8
  • C 𝑥 = 4 and 𝑦 = 4
  • D 𝑥 = 2 and 𝑦 = 2
  • E 𝑥 = 3 and 𝑦 = 4

Q10:

Using elimination, solve the simultaneous equations

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

Q11:

Using elimination, solve the simultaneous equations

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

Q12:

Using elimination, solve the simultaneous equations

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

Q13:

Use the elimination method to solve the simultaneous equations

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

Q14:

Use the elimination method to solve the simultaneous equations

  • A 𝑥 = 1 2 and 𝑦 = 1 8
  • B 𝑥 = 2 and 𝑦 = 6
  • C 𝑥 = 1 and 𝑦 = 3
  • D 𝑥 = 3 and 𝑦 = 1
  • E 𝑥 = 6 and 𝑦 = 2

Q15:

Solve the simultaneous equations 𝑥 6 + 𝑦 6 = 1 and 𝑥 6 + 𝑦 9 = 1 7 2 .

  • A 𝑥 = 1 4 1 , 𝑦 = 1 4 7
  • B 𝑥 = − 1 3 5 , 𝑦 = 1 4 1
  • C 𝑥 = 1 4 7 , 𝑦 = 1 4 1
  • D 𝑥 = 1 4 1 , 𝑦 = − 1 3 5

Q16:

Using elimination, solve the simultaneous equations

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

Q17:

Using elimination, solve the simultaneous equations

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

Q18:

Using elimination, solve the simultaneous equations

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

Q19:

Using elimination, solve the simultaneous equations

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

Q20:

Given that ( 𝑥 + 𝑦 , − 9 ) = ( 5 , 𝑥 − 𝑦 ) , what is ( 𝑦 , 𝑥 ) ?

  • A ( 5 , − 9 )
  • B ( − 2 , 7 )
  • C ( − 9 , 5 )
  • D ( 7 , − 2 )

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