## Precalculus (6th Edition) Blitzer

To get the point of intersection of the equations $x+2y=2$ and $x-2y=6$, first plot the graph with some steps which are as follows. Put $x=0$ and get the y-intercept for $x+2y=2$. \begin{align} & x+2y=2 \\ & 0+2y=2 \\ & 2y=2 \\ & y=1 \end{align} Hence, the graph passes through the point $\left( 0,1 \right)$. Put $y=0$ and get the x-intercept for $x+2y=2$. \begin{align} & x+2y=2 \\ & x+2\times 0=2 \\ & x=2 \end{align} Hence the graph passes through the point $\left( 2,0 \right)$. Again, Put $x=0$ and get the y-intercept for $x-2y=6$. \begin{align} & x-2y=6 \\ & 0-2y=6 \\ & -2y=6 \\ & y=-3 \end{align} Hence the graph passes through the point $\left( 0,-3 \right)$. And put $y=0$ and get the x-intercept for $x-2y=6$. \begin{align} & x-2y=6 \\ & x-2\times 0=6 \\ & x=6 \end{align} Thus, the graph passes through the point $\left( 6,0 \right)$. Now, plot the graph of the equations $x+2y=2$ and $x-2y=6$, and get the intersection point.