Worksheet: Solving Systems of Linear Equations Using Substitution

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

Q1:

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

  • A 5 2
  • B 9 5
  • C 5 9
  • D βˆ’ 1

Q2:

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

  • A π‘₯ = βˆ’ 2 , 𝑦 = βˆ’ 2 0
  • B π‘₯ = 8 , 𝑦 = βˆ’ 2
  • C π‘₯ = βˆ’ 2 , 𝑦 = 0
  • D π‘₯ = 0 , 𝑦 = βˆ’ 2
  • E π‘₯ = βˆ’ 2 , 𝑦 = 8

Q3:

Solve the simultaneous equations 2π‘₯+𝑦=11 and π‘₯βˆ’2𝑦=3.

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

Q4:

Solve the simultaneous equations π‘₯βˆ’π‘¦=4 and π‘₯+𝑦=14.

  • A π‘₯ = 9 , 𝑦 = 5
  • B π‘₯ = 5 , 𝑦 = 9
  • C π‘₯ = 2 3 , 𝑦 = 9
  • D π‘₯ = 9 , 𝑦 = 2 3

Q5:

Anthony and Benjamin each have a marble collection to sell. Benjamin has 1 more than 3 times the number of marbles Anthony has. How many marbles does each boy have to sell if the total number of marbles is 113?

  • AAnthony: 76, Benjamin: 37
  • BAnthony: 56, Benjamin: 57
  • CAnthony: 37, Benjamin: 76
  • DAnthony: 85, Benjamin: 28
  • EAnthony: 28, Benjamin: 85

Q6:

Find two numbers whose sum is 28 and difference is 13.

  • A20, 8
  • B41, 28
  • C 4 1 2 , 1 5 2
  • D βˆ’ 2 0 , 8

Q7:

The difference between two numbers is 9. Twice the sum of the two numbers is 10. Find the two numbers.

  • A βˆ’ 4 , 5
  • B2, 7
  • C βˆ’ 1 , 6
  • D βˆ’ 2 , 7

Q8:

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

  • A π‘₯ = βˆ’ 9 9 , 𝑦 = 2 9
  • B π‘₯ = 2 9 , 𝑦 = βˆ’ 9 9
  • C π‘₯ = 1 2 , 𝑦 = βˆ’ 3 1
  • D π‘₯ = βˆ’ 3 1 , 𝑦 = 1 2

Q9:

Find the values of π‘Ž and 𝑏, given the arithmetic mean between π‘Ž and 𝑏 is 58 and the arithmetic mean between 4π‘Ž and 8𝑏 is 350.

  • A π‘Ž = 5 7 2 , 𝑏 = 5 9 2
  • B π‘Ž = 5 7 , 𝑏 = 5 9
  • C π‘Ž = 1 4 6 , 𝑏 = βˆ’ 3 0
  • D π‘Ž = 2 2 8 , 𝑏 = 4 7 2
  • E π‘Ž = βˆ’ 3 0 , 𝑏 = 1 4 6

Q10:

Find the values of π‘Ž and 𝑏, given the arithmetic mean between π‘Ž and 𝑏 is βˆ’34 and the arithmetic mean between 4π‘Ž and 2𝑏 is βˆ’76.

  • A βˆ’ 6 , βˆ’ 6 2
  • B βˆ’ 8 , βˆ’ 6 0
  • C βˆ’ 7 , βˆ’ 5 9
  • D βˆ’ 9 , βˆ’ 6 1

Q11:

Find the values of π‘₯ and 𝑦, given the arithmetic mean between π‘₯ and 𝑦 is 77.5 and the arithmetic mean between 7π‘₯ and 6𝑦 is 467.

  • A π‘₯ = 7 6 , 𝑦 = 6 7
  • B π‘₯ = 1 , 𝑦 = 1 5 4
  • C π‘₯ = 7 , 𝑦 = 1 4 8
  • D π‘₯ = 4 , 𝑦 = 1 5 1

Q12:

If 7π‘₯βˆ’4𝑦=8 and π‘₯=4, what is the value of 𝑦?

Q13:

Given that (βˆ’2π‘Ž,8)=(2π‘βˆ’2,π‘Ž), find the values of π‘Ž and 𝑏.

  • A π‘Ž = 8 , 𝑏 = 7
  • B π‘Ž = βˆ’ 8 , 𝑏 = βˆ’ 7
  • C π‘Ž = 8 , 𝑏 = βˆ’ 7
  • D π‘Ž = βˆ’ 7 , 𝑏 = 8

Q14:

If π‘₯+𝑦=70 and π‘₯=47, what is the value of 𝑦?

Q15:

Solve the simultaneous equations 𝑦=5π‘₯+8,𝑦=βˆ’2π‘₯+1 by first finding an equation in π‘₯ and then 𝑦.

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

Q16:

If 7π‘₯βˆ’π‘¦=21 and 𝑦=4π‘₯, find π‘₯.

Q17:

Solve the simultaneous equations 𝑦=5π‘₯+3,𝑦=βˆ’π‘₯+9 by first finding an equation in terms of π‘₯ and then substituting your value of π‘₯ to find 𝑦.

  • A π‘₯ = 1 , 𝑦 = 8
  • B π‘₯ = βˆ’ 1 , 𝑦 = βˆ’ 2
  • C π‘₯ = 1 , 𝑦 = 1 0
  • D π‘₯ = 3 , 𝑦 = 6
  • E π‘₯ = βˆ’ 1 , 𝑦 = 8

Q18:

David’s father’s age equals David’s age multiplied by 10. If difference between their ages is 18 years, how old are they?

  • A2, 22
  • B3, 23
  • C2, 20
  • D12, 30

Q19:

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

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

Q20:

Solve the following system of equations: 4π‘₯+3𝑦=14,5π‘₯+2𝑦=14.

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

Q21:

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

Q22:

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.

  • A 22 years, 70 years
  • B 16 years, 41 years
  • C 16 years, 35 years
  • D 22 years, 41 years

Q23:

A movie theater sold 1,200 tickets. If a child’s ticket costs $5.95, an adult’s ticket costs $11.15, and the total revenue was $12,756, how many of each type of ticket did they sell?

  • A120 child tickets, 1,080 adult tickets
  • B200 child tickets, 1,000 adult tickets
  • C1,080 child tickets, 120 adult tickets
  • D1,000 child tickets, 200 adult tickets

Q24:

Solve the simultaneous equations 2π‘₯βˆ’π‘¦=14 and 2π‘¦βˆ’3π‘₯=5.

  • A π‘₯ = 8 0 , 𝑦 = 3 3
  • B π‘₯ = 4 7 , 𝑦 = 3 3
  • C π‘₯ = 3 3 , 𝑦 = 5 2
  • D π‘₯ = 3 3 , 𝑦 = 6 6
  • E π‘₯ = 5 2 , 𝑦 = 3 3

Q25:

If the equation 8π‘₯+6=38 has the same solution set as the equation π‘Žπ‘₯βˆ’18=π‘Ž, what is the value of π‘Ž?

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