Worksheet: Solving a System of Two Equations Using Matrices

In this worksheet, we will practice using matrices to solve a system of two linear equations.

Q1:

Express the given simultaneous equations as a matrix equation.

  • A 4 3 2 0 𝑥 𝑦 = 1 1 0
  • B 4 2 5 3 𝑥 𝑦 = 1 1 0
  • C 4 3 2 0 𝑥 𝑦 = 0 1 1
  • D 4 2 5 3 𝑥 𝑦 = 0 1 1
  • E 2 4 3 5 𝑥 𝑦 = 1 1 0

Q2:

Use matrices to solve the following system of equations.

  • A
  • B
  • C
  • D
  • E

Q3:

Use matrices to solve the system

  • A 𝑥 = 1 6 7 , 𝑦 = 8 7
  • B 𝑥 = 2 , 𝑦 = 1
  • C 𝑥 = 8 7 , 𝑦 = 1 6 7
  • D 𝑥 = 1 6 7 , 𝑦 = 8 7
  • E 𝑥 = 5 , 𝑦 = 1 3 5

Q4:

Express the given simultaneous equations as a matrix equation.

  • A
  • B
  • C
  • D
  • E

Q5:

Express the given simultaneous equations as a matrix equation.

  • A
  • B
  • C
  • D
  • E

Q6:

Express the given simultaneous equations as a matrix equation.

  • A
  • B
  • C
  • D
  • E

Q7:

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

Q8:

Use matrices to solve the following system of equations.

  • A
  • B
  • C
  • D
  • E

Q9:

Use matrices to solve the following system of equations.

  • A
  • B
  • C
  • D
  • E

Q10:

Use matrices to solve the following system of equations.

  • A
  • B
  • C
  • D
  • E

Q11:

Use matrices to solve the system

  • A 𝑥 = 1 , 𝑦 = 2
  • B 𝑥 = 2 7 4 3 , 𝑦 = 5 4 4 3
  • C 𝑥 = 2 , 𝑦 = 1
  • D 𝑥 = 1 , 𝑦 = 2
  • E 𝑥 = 1 0 , 𝑦 = 1 5

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