# Lesson Worksheet: Cramer’s Rule Mathematics

In this worksheet, we will practice using Cramer’s rule to solve a system of linear equations.

**Q1: **

Jacob is solving simultaneous equations using Cramer’s rule. He writes down

What does he write down for ?

- A
- B
- C
- D
- E

**Q3: **

Use determinants to solve the system

- A
- B
- C
- D
- E

**Q5: **

Use determinants to solve the system

- A,
- B,
- C,
- D,
- E,

**Q6: **

Use determinants to solve the system

- A,
- B,
- C,
- D,
- E,

**Q8: **

Solve, using Cramer's rule, the simultaneous equations

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q9: **

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.

- AA sketchbook costs 9 LE and a crayon costs 2.70 LE.
- BA sketchbook costs 22 LE and a crayon costs 9 LE.
- CA sketchbook costs 441 LE and a crayon costs 9 LE.
- DA sketchbook costs 22 LE and a crayon costs 1,078 LE.
- EA sketchbook costs 441 LE and a crayon costs 1,078 LE.

**Q10: **

Use Cramer’s rule to solve the simultaneous equations

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q11: **

Use determinants to solve the system

- A, ,
- B, ,
- C, ,
- D, ,

**Q13: **

Use determinants to solve the system

- A,
- B,
- C,
- D,
- E,

**Q14: **

Use determinants to solve the system

- A,
- B,
- C,
- D,
- E,

**Q15: **

True or False: Suppose that is a system of equations with . Then

- AFalse
- BTrue

**Q16: **

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

- AYes
- BNo

**Q17: **

True or False: In Cramer’s rule, .

- AFalse
- BTrue

**Q18: **

True or False: Cramer’s rule is used to determine solutions to linear systems when the determinant of the coefficient matrix equals zero.

- ATrue
- BFalse

**Q19: **

Noah is solving simultaneous equations using Cramer’s rule. He writes down the following:

What does he write down for ?

- A
- B
- C
- D
- E

**Q20: **

Use Cramer’s rule to solve the linear system of equations that is in matrix form:

- A,
- B,
- C,
- D,
- E,

**Q21: **

Complete the following: In Cramer’s rule, .

- A
- B
- C

**Q22: **

According to Cramer’s rule and given that

write the simultaneous equations of the system.

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q23: **

In Cramer’s rule, given that find the value of and .

- A,
- B,
- C,
- D,
- E,

**Q24: **

According to Cramer’s rule and given that write the simultaneous equations of the system.

- A,
- B,
- C,
- D,
- E,

**Q25: **

Consider the following linear system of equations in matrix form:

Write the determinant .

- A
- B
- C
- D
- E

Write the determinant .

- A
- B
- C
- D
- E

Write the determinant .

- A
- B
- C
- D
- E

Write the determinant .

- A
- B
- C
- D
- E