Question

graph and determine the solution of the system of equations.
x + 4y = 0
20y = -5x

use the graphing tool to graph the system.

Explanation:

Step1: Rewrite first equation to slope-intercept form

Solve $x + 4y = 0$ for $y$:
$4y = -x$
$y = -\frac{1}{4}x$

Step2: Rewrite second equation to slope-intercept form

Solve $20y = -5x$ for $y$:
$y = \frac{-5x}{20}$
$y = -\frac{1}{4}x$

Step3: Analyze the two equations

Both equations simplify to the same linear equation $y = -\frac{1}{4}x$, meaning they represent the exact same line. Every point on this line is a solution to the system.

Answer:

All points on the line $y = -\frac{1}{4}x$ (infinitely many solutions, as the two equations are identical when simplified).