Question

question
solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x + 4$
$x + y = -8$
plot two lines by clicking the graph.
click a line to delete it.
answer
attempt 1 out of 2
solution:

Explanation:

Step1: Find intercepts for $y=\frac{1}{2}x+4$

• x-intercept: Set $y=0$, solve $0=\frac{1}{2}x+4$

$\frac{1}{2}x=-4 \implies x=-8$, so point $(-8, 0)$

• y-intercept: Set $x=0$, $y=4$, so point $(0, 4)$

Step2: Rewrite second equation to slope-intercept

$x+y=-8 \implies y=-x-8$

Step3: Find intercepts for $y=-x-8$

• x-intercept: Set $y=0$, solve $0=-x-8$

$x=-8$, so point $(-8, 0)$

• y-intercept: Set $x=0$, $y=-8$, so point $(0, -8)$

Step4: Find intersection (system solution)

Set $\frac{1}{2}x+4 = -x-8$
$\frac{1}{2}x+x = -8-4$
$\frac{3}{2}x = -12$
$x = -12 \times \frac{2}{3} = -8$
Substitute $x=-8$ into $y=\frac{1}{2}x+4$: $y=\frac{1}{2}(-8)+4=-4+4=0$

Answer:

The solution to the system is $(-8, 0)$
To graph:

1. For $y=\frac{1}{2}x+4$, plot points $(-8, 0)$ and $(0, 4)$, then draw the line through them.
2. For $x+y=-8$, plot points $(-8, 0)$ and $(0, -8)$, then draw the line through them.

The lines intersect at $(-8, 0)$.