Question

solve the following system of equations graphically on the set of axes below.
$y = -dfrac{1}{3}x + 3$
$3x - y = 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

$3x - y = 7$ rearranges to $y = 3x - 7$

Step2: Find points for first line

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

• When $x=0$, $y=3$ → $(0, 3)$
• When $x=9$, $y=0$ → $(9, 0)$

Step3: Find points for second line

For $y = 3x - 7$:

• When $x=0$, $y=-7$ → $(0, -7)$
• When $x=3$, $y=2$ → $(3, 2)$

Step4: Find intersection algebraically

Set $-\frac{1}{3}x + 3 = 3x - 7$
Multiply by 3: $-x + 9 = 9x - 21$
$9 + 21 = 9x + x$ → $30 = 10x$ → $x=3$
Substitute $x=3$: $y = 3(3)-7=2$

Answer:

The solution (intersection point) is $(3, 2)$
To graph:

1. Plot $(0, 3)$ and $(9, 0)$, draw the line for $y = -\frac{1}{3}x + 3$
2. Plot $(0, -7)$ and $(3, 2)$, draw the line for $y = 3x - 7$

The lines intersect at $(3, 2)$