Worksheet: Solving Systems of Linear Equations Using Elimination

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

Q1:

Use the elimination method to solve the simultaneous equations π‘₯βˆ’2𝑦=βˆ’2,2π‘₯+3𝑦=10.

  • Aπ‘₯=1 and 𝑦=βˆ’1
  • Bπ‘₯=βˆ’16 and 𝑦=βˆ’14
  • Cπ‘₯=1 and 𝑦=1
  • Dπ‘₯=βˆ’14 and 𝑦=βˆ’16
  • Eπ‘₯=2 and 𝑦=2

Q2:

Use the elimination method to solve the simultaneous equations 5π‘₯+𝑦=20,4π‘₯+5𝑦=37.

  • Aπ‘₯=2 and 𝑦=6
  • Bπ‘₯=6 and 𝑦=8
  • Cπ‘₯=3 and 𝑦=5
  • Dπ‘₯=2 and 𝑦=10
  • Eπ‘₯=3 and 𝑦=25

Q3:

Using elimination, solve the simultaneous equations 3π‘₯+7𝑦=34,9π‘₯+10𝑦=91.

  • Aπ‘₯=9,𝑦=βˆ’1
  • Bπ‘₯=9,𝑦=1
  • Cπ‘₯=19,𝑦=11
  • Dπ‘₯=17,𝑦=1
  • Eπ‘₯=17,𝑦=4

Q4:

Using elimination, solve the simultaneous equations βˆ’5π‘₯+7𝑦=9,15π‘₯+12𝑦=39.

  • Aπ‘₯=2,𝑦=2
  • Bπ‘₯=2,𝑦=1
  • Cπ‘₯=2,𝑦=4
  • Dπ‘₯=1,𝑦=βˆ’2
  • Eπ‘₯=1,𝑦=2

Q5:

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

  • Aπ‘₯=3 and 𝑦=4
  • Bπ‘₯=2 and 𝑦=2
  • Cπ‘₯=8 and 𝑦=βˆ’4
  • Dπ‘₯=βˆ’4 and 𝑦=4
  • Eπ‘₯=4 and 𝑦=3

Q6:

Use the elimination method to solve the given simultaneous equations. βˆ’3π‘₯+4𝑦=6βˆ’2π‘₯βˆ’3𝑦=βˆ’13

  • Aπ‘₯=4 and 𝑦=6
  • Bπ‘₯=3 and 𝑦=11
  • Cπ‘₯=3 and 𝑦=2
  • Dπ‘₯=11 and 𝑦=3
  • Eπ‘₯=2 and 𝑦=3

Q7:

Use the elimination method to solve the simultaneous equations 4π‘₯βˆ’2𝑦=4,5π‘₯+3𝑦=16.

  • Aπ‘₯=12 and 𝑦=22
  • Bπ‘₯=3 and 𝑦=4
  • Cπ‘₯=2 and 𝑦=2
  • Dπ‘₯=4 and 𝑦=4
  • Eπ‘₯=10 and 𝑦=18

Q8:

Using elimination, solve the simultaneous equations 4π‘₯+6𝑦=40,3π‘₯+7𝑦=40.

  • Aπ‘₯=2,𝑦=4
  • Bπ‘₯=4,𝑦=βˆ’8
  • Cπ‘₯=8,𝑦=12
  • Dπ‘₯=4,𝑦=4
  • Eπ‘₯=1,𝑦=6

Q9:

Using elimination, solve the simultaneous equations 4π‘₯+6𝑦=20,3π‘₯βˆ’4𝑦=βˆ’2.

  • Aπ‘₯=4,𝑦=2
  • Bπ‘₯=2,𝑦=2
  • Cπ‘₯=2,𝑦=βˆ’4
  • Dπ‘₯=9,𝑦=9
  • Eπ‘₯=4,𝑦=6

Q10:

Using elimination, solve the simultaneous equations 5π‘₯+4𝑦=27,3π‘₯+12𝑦=45.

  • Aπ‘₯=1,𝑦=3
  • Bπ‘₯=3,𝑦=3
  • Cπ‘₯=3,𝑦=1
  • Dπ‘₯=5,𝑦=5
  • Eπ‘₯=7,𝑦=2

Q11:

Use the elimination method to solve the simultaneous equations 6π‘₯βˆ’3𝑦=18,5π‘₯+3𝑦=37.

  • Aπ‘₯=4 and 𝑦=6
  • Bπ‘₯=5 and 𝑦=4
  • Cπ‘₯=6 and 𝑦=4
  • Dπ‘₯=5 and 𝑦=3
  • Eπ‘₯=4 and 𝑦=5

Q12:

Use the elimination method to solve the simultaneous equations 6π‘₯βˆ’4𝑦=14,4π‘₯βˆ’4𝑦=8.

  • Aπ‘₯=1 and 𝑦=3
  • Bπ‘₯=6 and 𝑦=2
  • Cπ‘₯=2 and 𝑦=6
  • Dπ‘₯=12 and 𝑦=18
  • Eπ‘₯=3 and 𝑦=1

Q13:

Using elimination, solve the simultaneous equations βˆ’5π‘₯+6𝑦=13,5π‘₯+2𝑦=11.

  • Aπ‘₯=1, 𝑦=3
  • Bπ‘₯=4, 𝑦=2
  • Cπ‘₯=1, 𝑦=2
  • Dπ‘₯=4, 𝑦=1
  • Eπ‘₯=βˆ’1, 𝑦=3

Q14:

Using elimination, solve the simultaneous equations 4π‘₯+4𝑦=12,3π‘₯+4𝑦=10.

  • Aπ‘₯=2, 𝑦=1
  • Bπ‘₯=βˆ’2, 𝑦=1
  • Cπ‘₯=2, 𝑦=βˆ’1
  • Dπ‘₯=1, 𝑦=2
  • Eπ‘₯=5, 𝑦=βˆ’2

Q15:

Using elimination, solve the simultaneous equations 3π‘₯+2𝑦=14,6π‘₯βˆ’2𝑦=22.

  • Aπ‘₯=2, 𝑦=1
  • Bπ‘₯=βˆ’4, 𝑦=βˆ’1
  • Cπ‘₯=12, 𝑦=βˆ’25
  • Dπ‘₯=4, 𝑦=2
  • Eπ‘₯=4, 𝑦=1

Q16:

Using elimination, solve the simultaneous equations 3π‘₯+4𝑦=7,3π‘₯+2𝑦=5.

  • Aπ‘₯=1, 𝑦=1
  • Bπ‘₯=4, 𝑦=5
  • Cπ‘₯=1, 𝑦=2
  • Dπ‘₯=2, 𝑦=2
  • Eπ‘₯=2, 𝑦=1

Q17:

Use the elimination method to solve the simultaneous equations 23π‘₯+34𝑦=1724,43π‘₯+53𝑦=32.

  • Aπ‘₯=1532 and 𝑦=112
  • Bπ‘₯=12 and 𝑦=12
  • Cπ‘₯=158 and 𝑦=12
  • Dπ‘₯=2 and 𝑦=2
  • Eπ‘₯=17 and 𝑦=112

Q18:

Use the elimination method to solve the simultaneous equations 3π‘Ž+2𝑏=14,4π‘Ž+2𝑏=16.

  • Aπ‘Ž=4 and 𝑏=1
  • Bπ‘Ž=2 and 𝑏=8
  • Cπ‘Ž=2 and 𝑏=4
  • Dπ‘Ž=3 and 𝑏=2
  • Eπ‘Ž=10 and 𝑏=2

Q19:

Using elimination, solve the simultaneous equations 5π‘₯βˆ’4𝑦=21,4π‘₯+12𝑦=32.

  • Aπ‘₯=5,𝑦=4
  • Bπ‘₯=4,𝑦=5
  • Cπ‘₯=4,𝑦=1
  • Dπ‘₯=1,𝑦=5
  • Eπ‘₯=5,𝑦=1

Q20:

Use the elimination method to solve the simultaneous equations 3π‘₯+4𝑦=18,3π‘₯+2𝑦=12.

  • Aπ‘₯=0 and 𝑦=6
  • Bπ‘₯=βˆ’4 and 𝑦=12
  • Cπ‘₯=2 and 𝑦=5
  • Dπ‘₯=βˆ’16 and 𝑦=30
  • Eπ‘₯=2 and 𝑦=3

Q21:

Use the elimination method to solve the simultaneous equations 3π‘Ž+4𝑏=14,βˆ’3π‘Ž+5𝑏=4.

  • Aπ‘Ž=3 and 𝑏=5
  • Bπ‘Ž=6 and 𝑏=βˆ’1
  • Cπ‘Ž=6 and 𝑏=2
  • Dπ‘Ž=3 and 𝑏=βˆ’1
  • Eπ‘Ž=2 and 𝑏=2

Q22:

Use the elimination method to solve the simultaneous equationsβˆ’3π‘Ž+4𝑏=4,βˆ’3π‘Ž+5𝑏=8.

  • Aπ‘Ž=4 and 𝑏=2
  • Bπ‘Ž=2 and 𝑏=2
  • Cπ‘Ž=12 and 𝑏=8
  • Dπ‘Ž=12 and 𝑏=10
  • Eπ‘Ž=4 and 𝑏=4

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.