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In this lesson, we will learn how to solve systems of linear equations in three variables that can have one solution, infinite solutions, or no solution.

Q1:

Solve the simultaneous equations

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.

Q3:

Given that the solution set of the simultaneous equations is { ( β 6 , 7 , 8 ) } , find the values of π , π , and π .

Q4:

Given that the solution set of the simultaneous equations is { ( 0 , π , π ) } , find the values of π , π , and π .

Q5:

Q6:

Q7:

Q8:

Q9:

Q10:

Q11:

Find the solution of the system of equations 6 5 π₯ + 8 4 π¦ + 1 6 π§ = 5 4 6 , 8 1 π₯ + 1 0 5 π¦ + 2 0 π§ = 6 8 2 , 8 4 π₯ + 1 1 0 π¦ + 2 1 π§ = 7 1 3 , giving your answer in terms of an arbitrary real number π‘ if necessary.

Q12:

Find the solution of the system of equations 9 π₯ β 2 π¦ + 4 π§ = β 1 7 , 1 3 π₯ β 3 π¦ + 6 π§ = β 2 5 , and β 2 π₯ β π§ = 3 , giving your answer in terms of an arbitrary real number π‘ if necessary.

Q13:

Find the solution of the system of equations 7 π₯ + 1 4 π¦ + 1 5 π§ = 2 2 , 2 π₯ + 4 π¦ + 3 π§ = 5 , 3 π₯ + 6 π¦ + 1 0 π§ = 1 3 , giving your answer in terms of an arbitrary real number π‘ if necessary.

Q14:

Find the solution of the system of equations 3 π₯ β π¦ + 4 π§ = 6 , π¦ + 8 π§ = 0 , β 2 π₯ + π¦ = β 4 , giving your answer in terms of an arbitrary real number π‘ if necessary.

Q15:

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.

Q16:

In the triangle π΄ π΅ πΆ , 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 6 1 β .

Q17:

Q18:

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