# How do you graph the system of linear inequalities x-y>7 and 2x+y<8?

See below:

#### Explanation:

$x - y > 7$
$2 x + y < 8$

Let's first graph the boundary lines for each graph, then figure out what needs to be shaded. To graph the boundary lines, I'll change the form of the equations to slope-intercept:

$x - y > 7$

$- y > - x + 7$

$y < x - 7$

graph{x-7[-40,40,-20,20]}

To shade, does the origin fall within the solution?

$0 < 0 - 7 \implies 0 < - 7 \textcolor{w h i t e}{000} \textcolor{red}{X}$

And so we shade the other side:

graph{y -x+7< 0[-40,40,-20,20]}

$2 x + y < 8$

$y < 2 x + 8$

graph{2x+8[-40,40,-20,20]}

Is the origin part of this solution?

0<2(0)+8=>0<8color(white)(000)color(green)root

graph{y-2x-8<0[-40,40,-20,20]}

To put the graphs together, you'll shade to the right of the line that is rightmost (so "above" the point of intersection, it's $x - y > 7$ and below the point of intersection it's $2 x + y < 8$).

The point of intersection sits at:

$x - 7 = y = 2 x + 8$

$\therefore x - 7 = 2 x + 8$

$x = - 15$

$- 15 - 7 = y = - 22$

$\therefore \left(- 15 , - 22\right)$