# Worksheet: Systems of Linear Equations in Three Variables

Q1:

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

Q2:

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 , ,

Q3:

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 , ,

Q4:

Solve the simultaneous equations

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q5:

Solve the simultaneous equations

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q6:

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

• 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:

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

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q10:

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 , ,

Q11:

Solve the simultaneous equations

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q12:

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 , ,

Q13:

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 , ,

Q14:

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 , ,

Q17:

Solve the simultaneous equations

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q18:

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.