Lesson Worksheet: Solving Systems of Linear Equations Using Substitution Mathematics • 8th Grade

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


Find π‘₯ given 2π‘₯βˆ’π‘¦=5 and 𝑦=7π‘₯.


Use substitution to solve the simultaneous equations 13π‘₯+23=𝑦,6π‘₯+35𝑦=645.

  • Aπ‘₯=2 and 𝑦=23
  • Bπ‘₯=6 and 𝑦=23
  • Cπ‘₯=2 and 𝑦=43
  • Dπ‘₯=4 and 𝑦=83
  • Eπ‘₯=6 and 𝑦=83


Solve the simultaneous equations 𝑦+4π‘₯=βˆ’8 and 𝑦=5π‘₯+10.

  • Aπ‘₯=βˆ’2, 𝑦=βˆ’20
  • Bπ‘₯=8, 𝑦=βˆ’2
  • Cπ‘₯=βˆ’2, 𝑦=0
  • Dπ‘₯=0, 𝑦=βˆ’2
  • Eπ‘₯=βˆ’2, 𝑦=8


Solve the simultaneous equations π‘₯+4𝑦=17 and 2π‘₯+7𝑦=5.

  • Aπ‘₯=βˆ’99, 𝑦=29
  • Bπ‘₯=29, 𝑦=βˆ’99
  • Cπ‘₯=12, 𝑦=βˆ’31
  • Dπ‘₯=βˆ’31, 𝑦=12


Solve the following system of equations: 5π‘₯βˆ’2𝑦=8,4π‘₯+3𝑦=11.

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


Find the number of solutions to the following system of equations: 𝑦=π‘₯+1,𝑦=βˆ’π‘₯+9.

  • A0 solutions
  • BInfinite solutions
  • C1 solution


Solve the following system of equations if possible: 𝑦=π‘₯+1,𝑦=π‘₯βˆ’9.

  • AThere are no solutions.
  • Bπ‘₯=βˆ’9, 𝑦=1
  • Cπ‘₯=9, 𝑦=1
  • Dπ‘₯=1, 𝑦=9
  • Eπ‘₯=βˆ’1, 𝑦=βˆ’9


Find the number of solutions to the following system of equations: 𝑦+2π‘₯=4,2𝑦+4π‘₯=8.

  • AInfinite solutions
  • B1 solution
  • C0 solutions


Two numbers have a sum of 56. If one number is one-third of the other, what are the numbers?

  • A14, 28
  • B18, 56
  • C27, 29
  • D18, 28
  • E14, 42


A man’s age is 9 more than 2 times his son’s age. Given that the sum of their ages is 57, find each of their ages.

  • A22 years, 70 years
  • B16 years, 41 years
  • C16 years, 35 years
  • D22 years, 41 years

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