Question

Use the matrix tool to solve the system of equations. Choose the correct ordered pair.3x + 5y = 42 6x + 5y = 54

Answer 1

Solutions

In Matrix we use initially based on systems of linear equations.The matrix method is similar to the method of Elimination as but is a lot cleaner than the elimination method.Solving systems of equations by Matrix Method involves expressing the system of equations in form of a matrix and then reducing that matrix into what is known as Row Echelon Form.

Calculations

⇒ Rewrite the linear equations above as a matrix


`\left[\begin{array}{ccc}3&5&42\\6&5&54\\\end{array}\right]`

⇒ Apply to Row₂ : Row₂ - 2 Row₁


`\left[\begin{array}{ccc}3&5&42\\0&-5&-30\\\end{array}\right]`

⇒ Simplify rows


`\left[\begin{array}{ccc}3&5&42\\0&1&6\\\end{array}\right]`

Note: The matrix is now in echelon form.
The steps below are for back substitution.

⇒ Apply to Row₁ : Row₁ - 5 Row₂


`\left[\begin{array}{ccc}3&0&12\\0&1&6\\\end{array}\right]`

⇒ Simplify rows


`\left[\begin{array}{ccc}1&0&4\\0&1&6\\\end{array}\right]`

⇒ Therefore,


`x=4 y = 6`