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.}$ 

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

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

$\text{ Simplify rows}$  

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

$\text{Therefore, the solution is}$ 

$x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}$