Question

the following system of equations graphically on the set of axes below.
$y = -2x - 4$
$x - y = 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

$x - y = 7 \implies y = x - 7$

Step2: Find points for $y=-2x-4$

When $x=0$, $y=-4$; when $x=-2$, $y=0$
Points: $(0, -4), (-2, 0)$

Step3: Find points for $y=x-7$

When $x=0$, $y=-7$; when $x=7$, $y=0$
Points: $(0, -7), (7, 0)$

Step4: Find intersection (solve system)

Set $-2x - 4 = x - 7$
$-2x - x = -7 + 4$
$-3x = -3 \implies x=1$
Substitute $x=1$: $y=1-7=-6$
Intersection: $(1, -6)$

Answer:

1. For $y=-2x-4$, plot the points $(0, -4)$ and $(-2, 0)$, then draw a line through them.
2. For $y=x-7$, plot the points $(0, -7)$ and $(7, 0)$, then draw a line through them.
3. The solution to the system is the intersection point $(1, -6)$.