Question

solve the following system of equations graphically on the set of axes below.
$y = -\frac{1}{3}x + 1$
$2x - y = 6$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Rearrange $2x - y = 6$ to $y=2x-6$.

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

• When $x=0$, $y=1$ → $(0,1)$
• When $x=3$, $y=-\frac{1}{3}(3)+1=0$ → $(3,0)$

Step3: Find points for $y=2x-6$

• When $x=0$, $y=-6$ → $(0,-6)$
• When $x=3$, $y=2(3)-6=0$ → $(3,0)$

Step4: Identify intersection point

The two lines meet at $(3,0)$.

Answer:

The solution to the system is $\boldsymbol{(3, 0)}$
To plot the lines:

1. For $y=-\frac{1}{3}x+1$, plot $(0,1)$ and $(3,0)$, then draw the line through them.
2. For $y=2x-6$, plot $(0,-6)$ and $(3,0)$, then draw the line through them.