# Worksheet: Systems of Equations with Substitution

Q1:

Find given and .

• A
• B
• C
• D
• E

Q2:

Find given and .

• A
• B
• C
• D

Q3:

Solve the simultaneous equations and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

Solve the simultaneous equations and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q5:

Solve the simultaneous equations and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q6:

Solve the simultaneous equations and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q7:

Solve the simultaneous equations and .

• A ,
• B ,
• C ,
• D ,
• E ,

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 , 8
• D ,

Q10:

Find the values of and , given the arithmetic mean between and is 62 and the arithmetic mean between and is .

• A ,
• B ,
• C ,
• D ,
• E ,

Q11:

Renatoβs fatherβs age equals Renatoβ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 and , find .

Q13:

A manβs age is 9 more than 2 times his sonβ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 , 6
• B , 5
• C2, 7
• D , 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 and have a sum of 82 and a product of . Write an equation which could be solved to find the possible values of .

• A
• B
• C
• D

Q17:

Solve the following system of equations:

• A ,
• B ,
• C ,
• D ,

Q18:

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

• A ,
• B ,
• C ,
• D ,

Q19:

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 ,

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
• C18, 28
• D14, 42
• E27, 29

Q22:

If and , what is the value of ?

Q23:

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 ,

Q24:

Given that , find the values of and .

• A ,
• B ,
• C ,
• D ,

Q25:

If and , what is the value of ?