In this worksheet, we will practice solving a system of equations by substituting one equation into the other.

**Q5: **

Shady and Maged each have a marble collection to sell. Maged has 1 more than 3 times the number of marbles Shady has. How many marbles does each boy have to sell if the total number of marbles is 113?

- AShady: 37, Maged: 76
- BShady: 85, Maged: 28
- CShady: 76, Maged: 37
- DShady: 28, Maged: 85
- EShady: 56, Maged: 57

**Q6: **

Find two numbers whose sum is 28 and difference is 13.

- A20, 8
- B41, 28
- C , 8
- D ,

**Q7: **

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

**Q9: **

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 ,

**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: **

Karimβs fatherβs age equals Karimβs age multiplied by 10. If difference between their ages is 18 years, how old are they?

- A12, 30
- B2, 22
- C3, 23
- D2, 20

**Q19: **

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

**Q20: **

Solve the following system of equations:

- A ,
- B ,
- C ,
- D ,

**Q21: **

Solve the following system of equations:

- A ,
- B ,
- C ,
- D ,

**Q22: **

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

**Q23: **

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.

- A 16 years, 35 years
- B 22 years, 70 years
- C 22 years, 41 years
- D 16 years, 41 years

**Q24: **

A movie theater sold 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?

- A200 child tickets, adult tickets
- B child tickets, 120 adult tickets
- C child tickets, 200 adult tickets
- D120 child tickets, adult tickets

**Q25: **

Solve the simultaneous equations and .

- A ,
- B ,
- C ,
- D ,
- E ,