Worksheet: Solving Systems of Linear Equations Using Substitution

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

Q1:

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

Q2:

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

Q3:

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

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

Q4:

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

  • Aπ‘₯=9, 𝑦=5
  • Bπ‘₯=5, 𝑦=9
  • Cπ‘₯=23, 𝑦=9
  • Dπ‘₯=9, 𝑦=23

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
  • C412, 152
  • Dβˆ’20, 8

Q7:

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

  • Aβˆ’4, 5
  • B2, 7
  • Cβˆ’1, 6
  • Dβˆ’2, 7

Q8:

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

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.

  • Aπ‘Ž=572, 𝑏=592
  • Bπ‘Ž=57, 𝑏=59
  • Cπ‘Ž=146, 𝑏=βˆ’30
  • Dπ‘Ž=228, 𝑏=472
  • Eπ‘Ž=βˆ’30, 𝑏=146

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.

  • Aβˆ’6, βˆ’62
  • Bβˆ’8, βˆ’60
  • Cβˆ’7, βˆ’59
  • Dβˆ’9, βˆ’61

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.

  • Aπ‘₯=76, 𝑦=67
  • Bπ‘₯=1, 𝑦=154
  • Cπ‘₯=7, 𝑦=148
  • Dπ‘₯=4, 𝑦=151

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.

  • Aπ‘Ž=8, 𝑏=7
  • Bπ‘Ž=βˆ’8, 𝑏=βˆ’7
  • Cπ‘Ž=8, 𝑏=βˆ’7
  • Dπ‘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.

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

  • Aπ‘₯=1, 𝑦=8
  • Bπ‘₯=βˆ’1, 𝑦=βˆ’2
  • Cπ‘₯=1, 𝑦=10
  • Dπ‘₯=3, 𝑦=6
  • Eπ‘₯=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.

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

Q20:

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

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

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

  • Aπ‘₯=80, 𝑦=33
  • Bπ‘₯=47, 𝑦=33
  • Cπ‘₯=33, 𝑦=52
  • Dπ‘₯=33, 𝑦=66
  • Eπ‘₯=52, 𝑦=33

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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