Lesson: Cramer's Rule

In this lesson, we will learn how to use Cramer's rule to solve a system of linear equations.

Sample Question Videos

  • 04:24

Worksheet: 17 Questions • 1 Video

Q1:

Is Cramer’s rule useful for finding solutions to systems of linear equations in which there is an infinite set of solutions?

Q2:

William is solving simultaneous equations using Cramer’s rule. He writes down Δ = | | 9 8 2 2 | | , Δ = | | 9 9 3 2 | | .

What does he write down for Δ ?

Q3:

Use determinants to solve the system 3 𝑥 + 2 𝑦 2 𝑧 1 = 0 , 3 𝑥 + 3 𝑦 3 𝑧 + 3 = 0 , 2 𝑥 + 4 𝑦 5 𝑧 + 1 = 0 .

Q4:

Use determinants to solve the system 3 𝑦 = 3 + 5 𝑧 + 5 𝑥 , 5 𝑥 = 4 𝑦 3 𝑧 , 2 𝑥 2 𝑦 + 2 𝑧 = 2 .

Q5:

Use determinants to solve the system 8 𝑥 4 𝑦 = 8 , 9 𝑥 6 𝑦 = 9 .

Q6:

Use determinants to solve the system 9 𝑥 = 8 + 8 𝑦 , 6 𝑦 = 7 + 3 𝑥 .

Q7:

Use determinants to solve the system 7 𝑥 + 2 𝑦 + 5 = 0 , 𝑥 + 8 𝑦 1 = 0 .

Q8:

Use determinants to solve the system 5 𝑥 = 2 𝑦 5 + 3 𝑧 , 3 𝑥 𝑦 + 1 = 2 𝑧 , 2 𝑦 𝑧 = 5 𝑥 + 3 .

Q9:

Solve the simultaneous equations | | | 1 𝑧 4 𝑦 | | | = 2 3 , | | | 2 𝑦 5 𝑥 | | | = 1 3 , | | 3 𝑥 5 𝑧 | | = 5 1 .

Q10:

11 sketchbooks and 15 crayons cost 377 LE, and 15 sketchbooks and 16 crayons cost 474 LE. Use Cramer’s rule to find the price of a sketchbook and the price of a crayon.

Q11:

Use Cramer’s rule to solve the simultaneous equations | | | 3 𝑦 2 𝑥 | | | = 9 , | | | 1 𝑧 1 𝑦 | | | = 1 , | | 4 𝑥 4 𝑧 | | = 2 .

Q12:

Use determinants to solve the system 𝑥 5 𝑦 + 3 𝑧 = 5 , 3 𝑥 4 𝑦 + 2 𝑧 = 5 , 𝑥 + 3 𝑦 2 𝑧 = 5 .

Q13:

True or False: Suppose that 𝑎 𝑥 + 𝑏 𝑦 = 𝑒 , 𝑐 𝑥 + 𝑑 𝑦 = 𝑓 is a system of equations with 𝑎 𝑑 𝑏 𝑐 = 1 . The solution vector is 𝑥 𝑦 = 𝑒 𝑏 𝑓 𝑑 . d e t

Q14:

Given that 9 𝑦 + 5 𝑥 = 8 and 1 𝑦 + 1 𝑥 = 1 , determine the values of 𝑥 and 𝑦 .

Q15:

Use determinants to solve the system 2 𝑥 2 𝑦 + 4 𝑧 + 2 = 0 , 5 𝑥 4 𝑦 + 2 𝑧 5 = 0 , 2 𝑥 + 3 𝑦 + 𝑧 2 = 0 .

Q16:

Use determinants to solve the system 5 𝑥 + 𝑦 2 = 0 , 9 𝑥 + 4 𝑦 + 1 = 0 .

Q17:

Use determinants to solve the system 5 𝑥 = 2 2 𝑦 , 6 𝑦 = 5 + 𝑥 .

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