# Worksheet: Systems of Linear Equations in Three Variables

In this worksheet, we will practice solving systems of linear equations in three variables that can have one solution, infinite solutions, or no solution.

**Q1: **

Solve the simultaneous equations

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

**Q2: **

The sum of the ages of three brothers is 123 years. The first brother is 3 years older than the second brother who is 9 years older than the third. Find their current ages.

- A 34 years, 37 years, 43 years
- B 34 years, 43 years, 46 years
- C 37 years, 40 years, 46 years
- D 37 years, 46 years, 49 years
- E 34 years, 37 years, 46 years

**Q4: **

Given that the solution set of the simultaneous equations is , find the values of , , and .

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

**Q5: **

Solve the simultaneous equations

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

**Q6: **

Solve the simultaneous equations

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

**Q7: **

Solve the simultaneous equations

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

**Q8: **

Solve the simultaneous equations

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

**Q9: **

Solve the simultaneous equations

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

**Q10: **

Solve the simultaneous equations

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

**Q11: **

Find the solution of the system of equations , , , giving your answer in terms of an arbitrary real number if necessary.

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

**Q12: **

Find the solution of the system of equations , , and , giving your answer in terms of an arbitrary real number if necessary.

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

**Q13: **

The sum of the length and width of a cuboid is 24 cm. Its width plus its height is 19 cm and the sum of its height and length is 31 cm. Calculate the volume of the cuboid.

**Q14: **

In the triangle , one of the angles is the arithmetic mean of the other two. Find each angle of the triangle given the difference between the smaller and larger angles is .

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

**Q15: **

Solve the simultaneous equations

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

**Q16: **

Solve the simultaneous equations

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

**Q18: **

Find the values of , , and given that , , and are factors of .

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

**Q19: **

Four times the weight of Michael is 150 pounds more than the weight of Victoria. Four times the weight of Victoria is 660 pounds less than seventeen times the weight of Michael. Four times the weight of Michael plus the weight of Benjamin equals 290 pounds. Liam would balance all three of the others. Find the weights of the four people.

- AMichaelβs weight = 60 lb, Victoriaβs weight = 90 lb, Liamβs weight = 200 lb, Benjaminβs weight = 50 lb
- BMichaelβs weight = 50 lb, Victoriaβs weight = 60 lb, Liamβs weight = 90 lb, Benjaminβs weight = 200 lb
- CMichaelβs weight = 90 lb, Victoriaβs weight = 60 lb, Liamβs weight = 50 lb, Benjaminβs weight = 200 lb
- DMichaelβs weight = 60 lb, Victoriaβs weight = 90 lb, Liamβs weight = 50 lb, Benjaminβs weight = 200 lb
- EMichaelβs weight = 90 lb, Victoriaβs weight = 60 lb, Liamβs weight = 200 lb, Benjaminβs weight = 50 lb