Chapter 13.6, Problem 26WE

To determine

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

Answer to Problem 26WE

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:

  $\begin{array}{l}2x+y=7\\ 3x+y=9\end{array}$

Calculation:

  $\begin{array}{l}2x+y=7\mathrm{......}\left(1\right)\\ 3x+y=9\mathrm{......}\left(2\right)\\ x=\frac{7-y}{2}\mathrm{......}\left(3\right)\end{array}$

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

  $\begin{array}{l}3\left(\frac{7-y}{2}\right)+y=9\\ 21-3y+2y=18\\ -y=18-21\\ -y=-3\\ y=3\end{array}$

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

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

The graph will be:

  

The intersection point is $\left(2,3\right)$