# 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.

• 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

Q3:

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

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

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 rectangular prism 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 rectangular prism.

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, ,

Q17:

Three numbers add up to 216. The sum of the first two numbers is 112 and the third number is 8 less than this sum. How many possible values are there for the numbers?

• A0
• B1
• Cinfinitely many

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.

• AMichaelβs weight = 90 lb, Victoriaβs weight = 60 lb, Liamβs weight = 200 lb, Benjaminβs weight = 50 lb
• BMichaelβs weight = 90 lb, Victoriaβs weight = 60 lb, Liamβs weight = 50 lb, Benjaminβs weight = 200 lb
• CMichaelβs weight = 60 lb, Victoriaβs weight = 90 lb, Liamβs weight = 200 lb, Benjaminβs weight = 50 lb
• DMichaelβs weight = 50 lb, Victoriaβs weight = 60 lb, Liamβs weight = 90 lb, Benjaminβs weight = 200 lb
• EMichaelβs weight = 60 lb, Victoriaβs weight = 90 lb, Liamβs weight = 50 lb, Benjaminβs weight = 200 lb