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Lesson Worksheet: Solving Systems of Linear Equations by Omitting a Variable Mathematics • 8th Grade

In this worksheet, we will practice solving systems of linear equations by omitting a variable.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

𝐴𝐡𝐢 is a triangle, where 𝐡𝐢=55 cm, π΄πΆβˆ’π΄π΅=13 cm, and the perimeter is 124 cm. Find the lengths of 𝐴𝐢 and 𝐴𝐡 giving the answers to the nearest centimeter.

  • A𝐴𝐢=41cm, 𝐴𝐡=28cm
  • B𝐴𝐢=96cm, 𝐴𝐡=28cm
  • C𝐴𝐢=41cm, 𝐴𝐡=54cm
  • D𝐴𝐢=28cm, 𝐴𝐡=41cm
  • E𝐴𝐢=15cm, 𝐴𝐡=28cm

This lesson includes 39 additional questions and 183 additional question variations for subscribers.

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