Question

solve this system of equations by graphing. first graph the equations, and then type the solution.
y = 3x - 1
y = -3x - 7
click to select points on the graph.

Explanation:

Step1: Find intercepts for $y=3x-1$

For x-intercept: set $y=0$,
$0=3x-1 \implies 3x=1 \implies x=\frac{1}{3}$
Point: $(\frac{1}{3}, 0)$
For y-intercept: set $x=0$,
$y=3(0)-1=-1$
Point: $(0, -1)$

Step2: Find intercepts for $y=-3x-7$

For x-intercept: set $y=0$,
$0=-3x-7 \implies 3x=-7 \implies x=-\frac{7}{3}$
Point: $(-\frac{7}{3}, 0)$
For y-intercept: set $x=0$,
$y=-3(0)-7=-7$
Point: $(0, -7)$

Step3: Find intersection algebraically

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

Answer:

The solution to the system is $(-1, -4)$
(Graph points: For $y=3x-1$, plot $(\frac{1}{3}, 0)$ and $(0, -1)$ and draw the line; for $y=-3x-7$, plot $(-\frac{7}{3}, 0)$ and $(0, -7)$ and draw the line, they intersect at $(-1, -4)$)