Question

solve the following system of equations graphically on the set of axes below.
$y = -\dfrac{1}{3}x + 5$
$2x - y = 2$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

$y=2x-2$

Step2: Find points for $y=-\frac{1}{3}x+5$

When $x=0$, $y=5$; when $x=3$, $y=4$. Points: $(0,5), (3,4)$

Step3: Find points for $y=2x-2$

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

Step4: Find intersection algebraically

Set $-\frac{1}{3}x+5=2x-2$
Multiply by 3: $-x+15=6x-6$
$15+6=6x+x$
$21=7x$
$x=3$
Substitute $x=3$: $y=2(3)-2=4$

Answer:

The solution is the intersection point $(3, 4)$
To plot the lines:

1. For $y=-\frac{1}{3}x+5$, plot $(0,5)$ and $(3,4)$, then draw the line through them.
2. For $y=2x-2$, plot $(0,-2)$ and $(2,2)$, then draw the line through them.

The lines intersect at $(3,4)$.