Question

kuta software - infinite pre - algebra
solving systems of equations by graphing
solve each system by graphing.

1. $y = \frac{1}{3}x - 4$

$y = -\frac{7}{3}x + 4$
(here is a coordinate grid with x - axis from - 5 to 5 and y - axis from - 5 to 5)

Explanation:

Step1: Find intercepts for first line

For $y=\frac{1}{3}x - 4$:

• x-intercept: set $y=0$, $0=\frac{1}{3}x - 4 \implies x=12$
• y-intercept: set $x=0$, $y=-4$

Step2: Find intercepts for second line

For $y=-\frac{7}{3}x + 4$:

• x-intercept: set $y=0$, $0=-\frac{7}{3}x + 4 \implies x=\frac{12}{7}\approx1.71$
• y-intercept: set $x=0$, $y=4$

Step3: Graph both lines

Plot intercepts for each line and draw the lines.

Step4: Find intersection point

Solve algebraically to verify:
Set $\frac{1}{3}x - 4 = -\frac{7}{3}x + 4$
$\frac{1}{3}x+\frac{7}{3}x=4+4$
$\frac{8}{3}x=8$
$x=3$
Substitute $x=3$ into $y=\frac{1}{3}x - 4$:
$y=\frac{1}{3}(3)-4=1-4=-3$
Intersection is $(3, -3)$

Answer:

$(3, -3)$