Question

solve the following system of equations graphically on the set of axes below.
$y = x - 8$
$2x + y = -5$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

$y = -2x -5$

Step2: Find points for $y=x-8$

When $x=0$, $y=-8$; when $y=0$, $x=8$. Points: $(0,-8), (8,0)$

Step3: Find points for $y=-2x-5$

When $x=0$, $y=-5$; when $y=0$, $x=-\frac{5}{2}=-2.5$. Points: $(0,-5), (-2.5,0)$

Step4: Find intersection algebraically

Set $x-8 = -2x-5$
$x+2x = -5+8$
$3x=3$
$x=1$
Substitute $x=1$ into $y=x-8$: $y=1-8=-7$

Answer:

The solution to the system is the intersection point $(1, -7)$.
To graph:

1. Plot the line $y=x-8$ using points $(0,-8)$ and $(8,0)$, then draw a line through them.
2. Plot the line $y=-2x-5$ using points $(0,-5)$ and $(-2.5,0)$, then draw a line through them.
3. The two lines intersect at $(1, -7)$.