Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{2}{3}x + 4$
$y = -2x - 4$
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 $y=\frac{2}{3}x+4$

• x-intercept: Set $y=0$:

$0=\frac{2}{3}x+4 \implies \frac{2}{3}x=-4 \implies x=-6$

• y-intercept: Set $x=0$:

$y=\frac{2}{3}(0)+4=4$
Points: $(-6,0)$ and $(0,4)$

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

• x-intercept: Set $y=0$:

$0=-2x-4 \implies 2x=-4 \implies x=-2$

• y-intercept: Set $x=0$:

$y=-2(0)-4=-4$
Points: $(-2,0)$ and $(0,-4)$

Step3: Graph lines and find intersection

Plot the two lines using their intercepts. Solve algebraically to verify the intersection:
Set $\frac{2}{3}x+4=-2x-4$
Multiply by 3: $2x+12=-6x-12$
$2x+6x=-12-12$
$8x=-24 \implies x=-3$
Substitute $x=-3$ into $y=-2x-4$:
$y=-2(-3)-4=6-4=2$
Intersection point: $(-3,2)$

Answer:

The solution to the system is $\boldsymbol{(-3, 2)}$
(To graph: Plot $(-6,0)$ and $(0,4)$ to draw $y=\frac{2}{3}x+4$; plot $(-2,0)$ and $(0,-4)$ to draw $y=-2x-4$; the lines cross at $(-3,2)$)