Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x - 5$
$y = -x + 4$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intercepts for $y=\frac{1}{2}x-5$

• x-intercept: Set $y=0$, solve $0=\frac{1}{2}x-5$ → $x=10$, point $(10,0)$
• y-intercept: Set $x=0$, $y=-5$, point $(0,-5)$

Step2: Find intercepts for $y=-x+4$

• x-intercept: Set $y=0$, solve $0=-x+4$ → $x=4$, point $(4,0)$
• y-intercept: Set $x=0$, $y=4$, point $(0,4)$

Step3: Find intersection algebraically

Set $\frac{1}{2}x-5=-x+4$
$\frac{1}{2}x+x=4+5$
$\frac{3}{2}x=9$
$x=6$
Substitute $x=6$ into $y=-x+4$: $y=-6+4=-2$

Answer:

The solution to the system is the point $(6, -2)$
(To graph: Plot $(10,0)$ and $(0,-5)$ then draw a line through them for $y=\frac{1}{2}x-5$; plot $(4,0)$ and $(0,4)$ then draw a line through them for $y=-x+4$; the lines intersect at $(6, -2)$)