Question

solve the following system of equations graphically on the set of axes below.
$y = -\frac{5}{2}x - 6$
$x - y = -1$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite second equation to slope-intercept form

Start with $x - y = -1$, rearrange to solve for $y$:
$y = x + 1$

Step2: Find points for $y=-\frac{5}{2}x-6$

Choose $x=0$: $y=-\frac{5}{2}(0)-6=-6$, so point $(0, -6)$
Choose $x=-2$: $y=-\frac{5}{2}(-2)-6=5-6=-1$, so point $(-2, -1)$

Step3: Find points for $y=x+1$

Choose $x=0$: $y=0+1=1$, so point $(0, 1)$
Choose $x=-2$: $y=-2+1=-1$, so point $(-2, -1)$

Step4: Identify intersection point

The two lines share the point $(-2, -1)$, which is the solution.

Answer:

The solution to the system is $x=-2$, $y=-1$, or the point $(-2, -1)$