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Worksheet: Solving a System of Two Equations Using Matrices

Q1:

Express the simultaneous equations as a matrix equation.

  • A  4 3 βˆ’ 2 0   π‘₯ 𝑦  =  βˆ’ 1 1 0 
  • B  4 βˆ’ 2 5 3   π‘₯ 𝑦  =  βˆ’ 1 1 0 
  • C  4 3 βˆ’ 2 0   π‘₯ 𝑦  =  0 βˆ’ 1 1 
  • D  4 βˆ’ 2 5 3   π‘₯ 𝑦  =  0 βˆ’ 1 1 
  • E  βˆ’ 2 4 3 5   π‘₯ 𝑦  =  βˆ’ 1 1 0 

Q2:

Use matrices to solve the system

  • A π‘₯ = 1 6 7 , 𝑦 = βˆ’ 8 7
  • B π‘₯ = 2 , 𝑦 = βˆ’ 1
  • C π‘₯ = 8 7 , 𝑦 = βˆ’ 1 6 7
  • D π‘₯ = βˆ’ 1 6 7 , 𝑦 = 8 7
  • E π‘₯ = 5 , 𝑦 = 1 3 5

Q3:

Use matrices to solve the system of equations

  • A  π‘₯ 𝑦  =  βˆ’ 8 4 
  • B  π‘₯ 𝑦  =  4 3 8 
  • C  π‘₯ 𝑦  =  βˆ’ 5 6 3 6 
  • D  π‘₯ 𝑦  =  4 2 
  • E  π‘₯ 𝑦  =  2 8 βˆ’ 1 8 

Q4:

Use matrices to solve the system

  • A π‘₯ = 1 , 𝑦 = βˆ’ 2
  • B π‘₯ = 2 7 4 3 , 𝑦 = βˆ’ 5 4 4 3
  • C π‘₯ = 2 , 𝑦 = βˆ’ 1
  • D π‘₯ = βˆ’ 1 , 𝑦 = 2
  • E π‘₯ = 1 0 , 𝑦 = βˆ’ 1 5

Q5:

Use matrices to solve the system of equations

  • A  π‘₯ 𝑦  =  1 8 4 
  • B  π‘₯ 𝑦  =  1 1 2 2 8 
  • C  π‘₯ 𝑦  =  9 3 
  • D  π‘₯ 𝑦  =  8 2 
  • E  π‘₯ 𝑦  =  2 1 8 

Q6:

Express the simultaneous equations as a matrix equation.

  • A  3 1 8 1   π‘₯ 𝑦  =  3 2 4 
  • B  3 8 1 1   π‘₯ 𝑦  =  3 2 4 
  • C  3 1 8 1   π‘₯ 𝑦  =  2 4 3 
  • D  3 8 1 1   π‘₯ 𝑦  =  2 4 3 
  • E  3 βˆ’ 8 1 βˆ’ 1   π‘₯ 𝑦  =  2 4 3 

Q7:

Express the simultaneous equations as a matrix equation.

  • A  2 1 1 1   π‘š 𝑛  =  2 1 
  • B  2 βˆ’ 1 βˆ’ 1 1   π‘š 𝑛  =  2 1 
  • C  2 1 1 1   π‘š 𝑛  =  1 2 
  • D  2 βˆ’ 1 βˆ’ 1 1   π‘š 𝑛  =  1 2 
  • E  2 βˆ’ 1 1 βˆ’ 1   π‘š 𝑛  =  1 2 

Q8:

Use matrices to solve the system of equations

  • A  π‘š 𝑛  =  1 3 
  • B  π‘š 𝑛  =  2 4 
  • C  π‘š 𝑛  =  βˆ’ 1 1 
  • D  π‘š 𝑛  =  3 5 
  • E  π‘š 𝑛  =  βˆ’ 2 0 

Q9:

Express the simultaneous equations as a matrix equation.

  • A  3 3 2 1   π‘₯ 𝑦  =  7 1 2 
  • B  3 2 3 1   π‘₯ 𝑦  =  7 1 2 
  • C  3 3 2 1   π‘₯ 𝑦  =  1 2 7 
  • D  3 2 3 1   π‘₯ 𝑦  =  1 2 7 
  • E  3 2 1 3   π‘₯ 𝑦  =  1 2 7 

Q10:

Consider the simultaneous equations

Express the given simultaneous equations as a matrix equation.

  • A  4 βˆ’ 2 3 5   π‘₯ 𝑦  =  βˆ’ 1 1 0 
  • B  4 βˆ’ 2 5 3   π‘₯ 𝑦  =  βˆ’ 1 1 0 
  • C  4 βˆ’ 2 3 5   π‘₯ 𝑦  =  0 βˆ’ 1 1 
  • D  4 βˆ’ 2 5 3   π‘₯ 𝑦  =  0 βˆ’ 1 1 
  • E  4 3 βˆ’ 2 5   π‘₯ 𝑦  =  0 βˆ’ 1 1 

Write down the inverse of the coefficient matrix.

  • A 1 2 2  3 2 βˆ’ 5 4 
  • B 1 1 4  5 2 βˆ’ 3 4 
  • C 1 2 6  5 2 βˆ’ 3 4 
  • D 1 2  3 2 βˆ’ 5 4 
  • E 1 2 6  3 2 βˆ’ 5 4 

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

  • A  π‘₯ 𝑦  =  1 βˆ’ 1 
  • B  π‘₯ 𝑦  =  1 2 
  • C  π‘₯ 𝑦  =  βˆ’ 1 βˆ’ 2 
  • D  π‘₯ 𝑦  =  2 1 
  • E  π‘₯ 𝑦  =  βˆ’ 1 βˆ’ 3 

Q11:

Use matrices to solve the following system of equations:

  • A  π‘₯ 𝑦  =  7 9 4 8 
  • B  π‘₯ 𝑦  =  6 3 
  • C  π‘₯ 𝑦  =  4 2 
  • D  π‘₯ 𝑦  =  8 1 
  • E  π‘₯ 𝑦  =  5 1 