Question

part 1 of 2
graph the system of equations, and de
x + 5y = 10
2x + 10y = 80
use the graphing tool to graph the syst
click to enlarge graph
click the graph to plot the second point on your line.
(0,8)
selected: line
tool

Explanation:

Step1: Rewrite first equation to slope-intercept form

Solve $x + 5y = 10$ for $y$:
$5y = -x + 10$
$y = -\frac{1}{5}x + 2$

Step2: Find intercepts for first line

x-intercept (set $y=0$):
$x + 5(0) = 10 \implies x=10$, point $(10, 0)$
y-intercept (set $x=0$):
$0 + 5y = 10 \implies y=2$, point $(0, 2)$

Step3: Rewrite second equation to slope-intercept form

Solve $2x + 10y = 80$ for $y$:
$10y = -2x + 80$
$y = -\frac{1}{5}x + 8$

Step4: Find intercepts for second line

x-intercept (set $y=0$):
$2x + 10(0) = 80 \implies x=40$, point $(40, 0)$
y-intercept (set $x=0$):
$2(0) + 10y = 80 \implies y=8$, point $(0, 8)$

Step5: Analyze the system

Both lines have slope $-\frac{1}{5}$, so they are parallel (no intersection).

Answer:

1. For $x+5y=10$, plot points $(10, 0)$ and $(0, 2)$, then draw the line through them.
2. For $2x+10y=80$, plot points $(40, 0)$ and $(0, 8)$, then draw the line through them.
3. The system has no solution (parallel lines).