# Lesson Worksheet: Solving a System of Two Equations Using a Matrix Inverse Mathematics • 10th Grade

In this worksheet, we will practice solving a system of two linear equations using the inverse of the matrix of coefficients.

Q1:

Given that determine the values of and .

• A,
• B,
• C,
• D,

Q2:

Given that what is the value of ?

Q3:

Consider the simultaneous equations

Express the given simultaneous equations as a matrix equation.

• A
• B
• C
• D
• E

Write down the inverse of the coefficient matrix.

• A
• B
• C
• D
• E

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

• A
• B
• C
• D
• E

Q4:

Use matrices to solve the system

• A,
• B,
• C,
• D,
• E,

Q5:

Given that find .

• A
• B
• C
• D

Q6:

Use matrices to solve the system of equations

• A
• B
• C
• D
• E

Q7:

Use matrices to solve the system of equations

• A
• B
• C
• D
• E

Q8:

The length of a rectangle is 6 cm more than twice its width, and twice its length is 39 cm more than its width. Given this, use matrices to determine the perimeter of the rectangle.

Q9:

A girl bought 6 kilograms of flour and 5 kilograms of butter for 503 LE, and her friend bought 4 kg of flour and 7 kg of butter for 669 LE. Using matrices, find the price per kilogram of both flour and butter.

• AA kilogram of flour costs 6 LE and a kilogram of butter costs 110 LE.
• BA kilogram of flour costs 91 LE and a kilogram of butter costs 8 LE.
• CA kilogram of flour costs 61 LE and a kilogram of butter costs 46 LE.
• DA kilogram of flour costs 8 LE and a kilogram of butter costs 91 LE.

Q10:

The straight line whose equation is passes through the two points and . Using matrices, find and .

• A,
• B,
• C,
• D,
• E,

This lesson includes 30 additional questions and 178 additional question variations for subscribers.