# 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.

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:

Solve the simultaneous equations and .

• A,
• B,
• C,
• D,

Q6:

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,

Q7:

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

• A,
• B,
• C,
• D,

Q8:

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,

Q9:

If and , what is the value of ?

Q10:

Given that , find the values of and .

• A,
• B,
• C,
• D,

Q11:

If and , what is the value of ?

Q12:

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

• A,
• B,
• C,
• D,
• E,

Q13:

If and , find .

Q14:

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,

Q15:

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

Q16:

Solve the following system of equations:

• A,
• B,
• C,
• D,

Q17:

Solve the following system of equations:

• A,
• B,
• C,
• D,

Q18:

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

Q19:

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

Q20:

Solve the simultaneous equations and .

• A,
• B,
• C,
• D,
• E,

Q21:

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

Q22:

Use substitution to solve the simultaneous equations

• A and
• B and
• C and
• D and
• E and

Q23:

Use substitution to solve the simultaneous equations

• A and
• B and
• C and
• D and
• E and

Q24:

Use substitution to solve the simultaneous equations to find and .

• A and
• B and
• C and
• D and
• E and

Q25:

If and , then .