Question

solve the following system of equations graphically on the set of axes below.
$y = -x + 2$
$2x - y = 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Rearrange $2x - y = 7$ to $y=mx+b$ form:
$y = 2x - 7$

Step2: Find points for $y=-x+2$

Identify intercepts:

• x-intercept: set $y=0$, $0=-x+2 \implies x=2$, point $(2, 0)$
• y-intercept: set $x=0$, $y=0+2=2$, point $(0, 2)$

Step3: Find points for $y=2x-7$

Identify intercepts:

• x-intercept: set $y=0$, $0=2x-7 \implies x=\frac{7}{2}=3.5$, point $(3.5, 0)$
• y-intercept: set $x=0$, $y=0-7=-7$, point $(0, -7)$

Step4: Find intersection algebraically

Set equations equal:
$-x+2 = 2x-7$
$-x-2x = -7-2$
$-3x = -9$
$x=3$
Substitute $x=3$ into $y=-x+2$:
$y=-3+2=-1$

Answer:

The system's solution (intersection point) is $(3, -1)$. To graph:

1. Plot the line $y=-x+2$ using points $(0,2)$ and $(2,0)$, then draw the line through them.
2. Plot the line $y=2x-7$ using points $(0,-7)$ and $(3.5,0)$, then draw the line through them.
3. The two lines cross at $(3, -1)$.