Question

solve the following system of equations graphically on the set of axes below.
$y = x - 3$
$x + 2y = 12$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

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

• x-intercept: Set $y=0$, $0=x-3 \implies x=3$, point $(3,0)$
• y-intercept: Set $x=0$, $y=0-3=-3$, point $(0,-3)$

Step2: Rewrite second equation to slope-intercept

$x+2y=12 \implies 2y=-x+12 \implies y=\frac{-x}{2}+6$

Step3: Find intercepts for $y=\frac{-x}{2}+6$

• x-intercept: Set $y=0$, $0=\frac{-x}{2}+6 \implies x=12$, point $(12,0)$
• y-intercept: Set $x=0$, $y=6$, point $(0,6)$

Step4: Find intersection algebraically (verify)

Substitute $y=x-3$ into $x+2y=12$:
$x+2(x-3)=12 \implies x+2x-6=12 \implies 3x=18 \implies x=6$
Then $y=6-3=3$

Answer:

The solution to the system is the point of intersection: $(6, 3)$

To graph:

1. Plot the line $y=x-3$ using points $(3,0)$ and $(0,-3)$
2. Plot the line $x+2y=12$ using points $(12,0)$ and $(0,6)$
3. The lines cross at $(6, 3)$