# 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

Q2:

Use determinants to solve the system

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q3:

Use determinants to solve the system

• A
• B
• C
• D
• E

Q4:

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,

Q7:

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, ,

Q12:

Use determinants to solve the system

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

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