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Worksheet: Systems of Equations with Substitution

In this worksheet, we will practice solving a system of equations by substituting one equation into the other.

Q1:

Find π‘₯ given 8 π‘₯ βˆ’ 𝑦 = 3 and 𝑦 = 3 π‘₯ .

  • A 5 3
  • B 3 1 1
  • C 1 1 3
  • D 3 5
  • E 3 8

Q2:

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

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

Q3:

Solve the simultaneous equations 𝑦 + 4 π‘₯ = βˆ’ 8 and 𝑦 = 5 π‘₯ + 1 0 .

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

Q4:

Solve the simultaneous equations 𝑦 βˆ’ 4 π‘₯ = βˆ’ 2 and 𝑦 = 6 π‘₯ + 4 .

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

Q5:

Solve the simultaneous equations 𝑦 βˆ’ 5 π‘₯ = βˆ’ 1 and 𝑦 = 8 π‘₯ βˆ’ 7 .

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

Q6:

Solve the simultaneous equations 𝑦 βˆ’ 5 π‘₯ = βˆ’ 1 and 𝑦 = 4 π‘₯ + 7 .

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

Q7:

Solve the simultaneous equations 𝑦 βˆ’ 5 π‘₯ = 4 and 𝑦 = 4 π‘₯ βˆ’ 3 .

  • A π‘₯ = βˆ’ 7 , 𝑦 = βˆ’ 1 0
  • B π‘₯ = βˆ’ 7 , 𝑦 = βˆ’ 2 5
  • C π‘₯ = βˆ’ 3 1 , 𝑦 = βˆ’ 7
  • D π‘₯ = βˆ’ 7 , 𝑦 = βˆ’ 3 1
  • E π‘₯ = βˆ’ 1 0 , 𝑦 = βˆ’ 7

Q8:

Solve the simultaneous equations by first finding an equation in and then .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q9:

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

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

Q10:

Find the values of π‘Ž and 𝑏 , given the arithmetic mean between π‘Ž and 𝑏 is 62 and the arithmetic mean between 2 π‘Ž and 3 𝑏 is 3 2 1 2 .

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

Q11:

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

  • A12, 30
  • B2, 22
  • C3, 23
  • D2, 20

Q12:

If 7 π‘₯ βˆ’ 𝑦 = 2 1 and 𝑦 = 4 π‘₯ , find π‘₯ .

Q13:

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

Q14:

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

  • A βˆ’ 1 , 6
  • B βˆ’ 4 , 5
  • C2, 7
  • D βˆ’ 2 , 7

Q15:

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

Q16:

Two integers π‘₯ and 𝑦 have a sum of 82 and a product of 1 6 8 0 . Write an equation which could be solved to find the possible values of π‘₯ .

  • A 8 2 π‘₯ = 1 6 8 0 π‘₯
  • B π‘₯ = 1 6 8 0 8 2
  • C π‘₯ 1 6 8 0 = 8 2
  • D π‘₯ ( 8 2 βˆ’ π‘₯ ) = 1 6 8 0

Q17:

Solve the following system of equations:

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

Q18:

Find the values of π‘Ž and 𝑏 , given the arithmetic mean between π‘Ž and 𝑏 is βˆ’ 3 4 and the arithmetic mean between 4 π‘Ž and 2 𝑏 is βˆ’ 7 6 .

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

Q19:

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

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

Q20:

Solve the following system of equations:

  • A π‘₯ = 2 , 𝑦 = βˆ’ 2
  • B π‘₯ = βˆ’ 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
  • C18, 28
  • D14, 42
  • E27, 29

Q22:

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

Q23:

Solve the simultaneous equations by first finding an equation in terms of π‘₯ and then substituting your value of π‘₯ to find 𝑦 .

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

Q24:

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

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

Q25:

If π‘₯ + 𝑦 = 7 0 and π‘₯ = 4 7 , what is the value of 𝑦 ?

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