Question

What is the solution to the system of equation

Answer 1

`x=(-2,(5)/(3) )`

Explanation:

1) We will use the matrix method to solve this problem.

`\left[\begin{array}{ccc}-2/3&1&3\\1&0&-2\\\end{array}\right]`

2) Swap Row₁ and Row₂ to make row reduction easier.

`\left[\begin{array}{ccc}1&0&-2\\-2/3&1&3\\\end{array}\right]`

3) Apply to Row₂ : Row₂ +
`(2)/(3)` Row₁.

`\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\end{array}\right]`

4) Simplify rows.

`\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right]`

Note: The matrix is now in row echelon form.

The steps below are for back substitution.

5) Apply Row₁ : Row₁ - 0 Row₂.

`\left[\begin{array}{ccc}1&0&-2\0\\0&1&5/3\end{array}\right]`

6) Simplify rows.

`\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right]`

Note: The matrix is now in reduced row echelon form.

7) Therefore,

`x=-2\\x=(5)/(3)`