Question

graph and determine the solution of the system of equations.
x + 4y = 0
20y = -5x
use the graphing tool to graph the system.
what is the solution? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is
(type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Rewrite first equation to slope-intercept

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

Step2: Rewrite second equation to slope-intercept

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

Step3: Compare the two equations

Both equations simplify to the same linear equation $y = -\frac{1}{4}x$, meaning they represent the same line. All points on the line satisfy both equations.

Answer:

B. There are infinitely many solutions.