Question

graph the system of equations, and determine the solution.
$x + 5y = 10$
$2x + 10y = 80$
use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Rewrite equations to slope-intercept form

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

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

Step2: Analyze line properties

Both lines have the same slope $m = -\frac{1}{5}$, different y-intercepts $(0,2)$ and $(0,8)$. Parallel lines never intersect.

Answer:

The system has no solution, as the two lines are parallel and do not intersect.