Chapter SH, Problem 8.3.12EP

To determine

To calculate: To find the four solution of equation and write the solution in ordered pair

Answer to Problem 8.3.12EP

Solutions of equation are $\left(0,-2\right),\left(1,-\frac{3}{2}\right),\left(2,-1\right),\left(3,-\frac{1}{2}\right)$

Explanation of Solution

Given information:Equation is $2x-4y=8$

Calculation:

Equation is given as

  $2x-4y=8$

Rewriting the equation as below

  $\begin{array}{l}4y=2x-8\\ y=\frac{2}{4}x-\frac{8}{4}\\ y=\frac{1}{2}x-2\end{array}$

When $x=0$

  $\begin{array}{l}y=\frac{1}{2}\left(0\right)-2\\ y=0-2\\ y=-2\end{array}$

When $x=1$

  $\begin{array}{l}y=\frac{1}{2}\left(1\right)-2\\ y=\frac{1}{2}-2\\ y=\frac{1-4}{2}\\ y=-\frac{3}{2}\end{array}$

When $x=2$

  $\begin{array}{l}y=\frac{1}{2}\left(2\right)-2\\ y=\frac{2}{2}-2\\ y=1-2\\ y=-1\end{array}$

When $x=3$

  $\begin{array}{l}y=\frac{1}{2}\left(3\right)-2\\ y=\frac{3}{2}-2\\ y=\frac{3-4}{2}\\ y=-\frac{1}{2}\end{array}$

Solution of the equation are $\left(0,-2\right),\left(1,-\frac{3}{2}\right),\left(2,-1\right),\left(3,-\frac{1}{2}\right)$

Conclusion:

Hence, solutions of equation are $\left(0,-2\right),\left(1,-\frac{3}{2}\right),\left(2,-1\right),\left(3,-\frac{1}{2}\right)$