Question

Solve the following system by any method -8x-8y=0 -8x+2y=-20

Answer 1

`\fbox{Solution by using Matrix}`


`\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20`


`\text{Rewrite the linear equations above as a matrix}`


`\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right]`


`\text{Apply to Row2 : Row2 + Row1}`


`\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right]`


`\text{ Simplify rows}`


`\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right]`


`\text{Note: The matrix is now in echelon form.}`
`\text{The steps below are for back substitution.}`


`\text{Apply to Row1 : Row1 + 8 Row2}`


`\left[\begin{array}{ccc}8&0&80/30\\0&1&10/3\\\end{array}\right]`


`\text{ Simplify rows}`


`\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right]`


`\text{Therefore, the solution is}`


`x= (10)/(3) \ \text{and} \ \ y=(10)/(3)`