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Worksheet: Solving Systems of Linear Equations by Elimination

Q1:

Solve the simultaneous equations π‘₯ βˆ’ 𝑦 = 8 and 3 π‘₯ βˆ’ 5 𝑦 + 1 0 = 0 .

  • A π‘₯ = 1 7 , 𝑦 = 2 5
  • B π‘₯ = βˆ’ 9 , 𝑦 = 1 7
  • C π‘₯ = 2 5 , 𝑦 = βˆ’ 1 7
  • D π‘₯ = 2 5 , 𝑦 = 1 7

Q2:

Use the elimination method to solve the simultaneous equations

  • A π‘₯ = βˆ’ 1 4 and 𝑦 = βˆ’ 1 6
  • B π‘₯ = βˆ’ 1 6 and 𝑦 = βˆ’ 1 4
  • C π‘₯ = 1 and 𝑦 = 1
  • D π‘₯ = 2 and 𝑦 = 2
  • E π‘₯ = 1 and 𝑦 = βˆ’ 1

Q3:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 1 7 , 𝑦 = 4
  • B π‘₯ = 9 , 𝑦 = βˆ’ 1
  • C π‘₯ = 1 7 , 𝑦 = 1
  • D π‘₯ = 9 , 𝑦 = 1
  • E π‘₯ = 1 9 , 𝑦 = 1 1

Q4:

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

  • A π‘₯ = 4 and 𝑦 = 3
  • B π‘₯ = βˆ’ 4 and 𝑦 = 4
  • C π‘₯ = 2 and 𝑦 = 2
  • D π‘₯ = 8 and 𝑦 = βˆ’ 4
  • E π‘₯ = 3 and 𝑦 = 4

Q5:

Use the elimination method to solve the simultaneous equations

  • A π‘₯ = 6 and 𝑦 = 8
  • B π‘₯ = 2 and 𝑦 = 1 0
  • C π‘₯ = 2 and 𝑦 = 6
  • D π‘₯ = 3 and 𝑦 = 5
  • E π‘₯ = 3 and 𝑦 = 2 5

Q6:

Use the elimination method to solve the given simultaneous equations.

  • A π‘₯ = 3 and 𝑦 = 2
  • B π‘₯ = 1 1 and 𝑦 = 3
  • C π‘₯ = 3 and 𝑦 = 1 1
  • D π‘₯ = 2 and 𝑦 = 3
  • E π‘₯ = 4 and 𝑦 = 6

Q7:

Use the elimination method to solve the simultaneous equations

  • A π‘₯ = 1 2 and 𝑦 = 2 2
  • B π‘₯ = 1 0 and 𝑦 = 1 8
  • C π‘₯ = 4 and 𝑦 = 4
  • D π‘₯ = 2 and 𝑦 = 2
  • E π‘₯ = 3 and 𝑦 = 4

Q8:

Solve the simultaneous equations π‘₯ 6 + 𝑦 6 = 1 and π‘₯ 6 + 𝑦 9 = 1 7 2 .

  • A π‘₯ = 1 4 1 , 𝑦 = 1 4 7
  • B π‘₯ = βˆ’ 1 3 5 , 𝑦 = 1 4 1
  • C π‘₯ = 1 4 7 , 𝑦 = 1 4 1
  • D π‘₯ = 1 4 1 , 𝑦 = βˆ’ 1 3 5

Q9:

Using elimination, solve the simultaneous equations

  • A π‘₯ = βˆ’ 1 , 𝑦 = 3
  • B π‘₯ = 1 , 𝑦 = 2
  • C π‘₯ = 4 , 𝑦 = 1
  • D π‘₯ = 1 , 𝑦 = 3
  • E π‘₯ = 4 , 𝑦 = 2

Q10:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 9 , 𝑦 = 9
  • B π‘₯ = 4 , 𝑦 = 6
  • C π‘₯ = 2 , 𝑦 = βˆ’ 4
  • D π‘₯ = 2 , 𝑦 = 2
  • E π‘₯ = 4 , 𝑦 = 2

Q11:

Using elimination, solve the simultaneous equations

  • A π‘₯ = βˆ’ 2 , 𝑦 = 1
  • B π‘₯ = 1 , 𝑦 = 2
  • C π‘₯ = 2 , 𝑦 = βˆ’ 1
  • D π‘₯ = 2 , 𝑦 = 1
  • E π‘₯ = 5 , 𝑦 = βˆ’ 2

Q12:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 2 , 𝑦 = 1
  • B π‘₯ = 4 , 𝑦 = 2
  • C π‘₯ = 1 2 , 𝑦 = βˆ’ 2 5
  • D π‘₯ = 4 , 𝑦 = 1
  • E π‘₯ = βˆ’ 4 , 𝑦 = βˆ’ 1

Q13:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 4 , 𝑦 = 5
  • B π‘₯ = 5 , 𝑦 = 4
  • C π‘₯ = 1 , 𝑦 = 5
  • D π‘₯ = 5 , 𝑦 = 1
  • E π‘₯ = 4 , 𝑦 = 1

Q14:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 4 , 𝑦 = 5
  • B π‘₯ = 2 , 𝑦 = 2
  • C π‘₯ = 2 , 𝑦 = 1
  • D π‘₯ = 1 , 𝑦 = 1
  • E π‘₯ = 1 , 𝑦 = 2

Q15:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 2 , 𝑦 = 4
  • B π‘₯ = 1 , 𝑦 = βˆ’ 2
  • C π‘₯ = 2 , 𝑦 = 2
  • D π‘₯ = 1 , 𝑦 = 2
  • E π‘₯ = 2 , 𝑦 = 1

Q16:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 3 , 𝑦 = 1
  • B π‘₯ = 7 , 𝑦 = 2
  • C π‘₯ = 1 , 𝑦 = 3
  • D π‘₯ = 3 , 𝑦 = 3
  • E π‘₯ = 5 , 𝑦 = 5

Q17:

Using elimination, solve the simultaneous equations

  • A π‘₯ = 8 , 𝑦 = 1 2
  • B π‘₯ = 4 , 𝑦 = βˆ’ 8
  • C π‘₯ = 2 , 𝑦 = 4
  • D π‘₯ = 4 , 𝑦 = 4
  • E π‘₯ = 1 , 𝑦 = 6

Q18:

Given that ( π‘₯ + 𝑦 , βˆ’ 9 ) = ( 5 , π‘₯ βˆ’ 𝑦 ) , what is ( 𝑦 , π‘₯ ) ?

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

Q19:

Find two numbers with a sum of 69 and a difference of 3.

  • A72, 33
  • B15, 54
  • C45, 33
  • D36, 33
  • E36, 3

Q20:

Solve the simultaneous equations 4 π‘₯ + 𝑦 = 7 and 8 π‘₯ βˆ’ 𝑦 = 4 1 .

  • A π‘₯ = 1 7 2 , 𝑦 = 5 5
  • B π‘₯ = 5 , 𝑦 = βˆ’ 1 3
  • C π‘₯ = 4 , 𝑦 = βˆ’ 5 5 3
  • D π‘₯ = 4 , 𝑦 = βˆ’ 9
  • E π‘₯ = 3 3 8 , 𝑦 = βˆ’ 8