Chapter 13.6, Problem 29WE

To determine

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

Answer to Problem 29WE

The value of $x=2$ and $y=-3$ and the intersection point is $\left(2,-3\right)$ .

Explanation of Solution

Given information: The equation is:

  $\begin{array}{l}4x+5y=-7\\ 2x-3y=13\end{array}$

Calculation:

  $\begin{array}{l}4x+5y=-7\mathrm{......}\left(1\right)\\ 2x-3y=13\mathrm{......}\left(2\right)\\ x\text{ =}\frac{-7-5y}{4}\mathrm{......}\left(3\right)\end{array}$

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

  $\begin{array}{l}2\left(\frac{-7-5y}{4}\right)-3y=13\\ -14-10y-12y=52\\ -22y=52+14\\ -22y=66\\ y=-\frac{66}{22}\\ y=-3\end{array}$

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 $\left(2,-3\right)$