# Worksheet: Solving Systems of Linear Equations Using Substitution

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

Q1:

Find given and .

Q2:

Solve the simultaneous equations and .

• A,
• B,
• C,
• D,
• E,

Q3:

Solve the simultaneous equations and .

• A,
• B,
• C,
• D,

Q4:

Solve the simultaneous equations and .

• A,
• B,
• C,
• D,

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,
• D, 8

Q7:

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

• A, 5
• B2, 7
• C, 6
• D, 7

Q8:

Solve the simultaneous equations and .

• A,
• B,
• C,
• D,

Q9:

Find the values of and , given the arithmetic mean between and is 58 and the arithmetic mean between and is 350.

• A,
• B,
• C,
• D,
• E,

Q10:

Find the values of and , given the arithmetic mean between and is and the arithmetic mean between and is .

• A,
• B,
• C,
• D,

Q11:

Find the values of and , given the arithmetic mean between and is 77.5 and the arithmetic mean between and is 467.

• A,
• B,
• C,
• D,

Q12:

If and , what is the value of ?

Q13:

Given that , find the values of and .

• A,
• B,
• C,
• D,

Q14:

If and , what is the value of ?

Q15:

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

• A,
• B,
• C,
• D,
• E,

Q16:

If and , find .

Q17:

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

• A,
• B,
• C,
• D,
• E,

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:

• A,
• B,
• C,
• D,

Q20:

Solve the following system of equations:

• A,
• B,
• C,
• D,

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 , 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 and .

• A,
• B,
• C,
• D,
• E,

Q25:

If the equation has the same solution set as the equation , what is the value of ?