# 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.

**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.

- A34 years, 37 years, 43 years
- B37 years, 46 years, 49 years
- C34 years, 37 years, 46 years
- D34 years, 43 years, 46 years
- E37 years, 40 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, ,

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