Chapter 13.6, Problem 30WE

To determine

To solve: the equation algebraically then draw the graph and also label the intersection point.

Answer to Problem 30WE

The value of $x=0$ and $y=4$ and the intersection point is $\left(0,4\right)$ .

Explanation of Solution

Given information: The equation is:

  $\begin{array}{l}3x+2y=8\\ -x+3y=12\end{array}$

Calculation:

  $\begin{array}{l}3x+2y=8\mathrm{......}\left(1\right)\\ -x+3y=12\mathrm{......}\left(2\right)\\ x\text{ =}\frac{8-2y}{3}\mathrm{......}\left(3\right)\end{array}$

Put value of $x$ in equation $\left(2\right)$

  $\begin{array}{l}-\frac{8-2y}{3}+3y=12\\ -8+2y+9y=36\\ 11y=36+8\\ 11y=44\\ y=\frac{44}{11}\\ y=4\end{array}$

Put value of $y$ in equation $\left(3\right)$

  $\begin{array}{l}x\text{ =}\frac{-7-5y}{4}\\ x\text{ =}\frac{-7-5\left(-3\right)}{4}\\ x=\frac{-7+15}{4}\\ x=\frac{8}{4}\\ x=2\end{array}$

The graph will be:

  

The intersection point is $\left(0,4\right)$