# Worksheet: Solving Systems of Linear Equations Using Substitution

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

**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

**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: **

Davidβs fatherβs age equals Davidβs 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 manβs age is 9 more than 2 times his sonβs 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 childβs ticket costs $5.95, an adultβs 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 ?