Question

graph and determine the solution of the system of equations
x + 6y = 0
18y = -3x
use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Rewrite to slope-intercept form

First equation: $x + 4y = 0$
$4y = -x$
$y = -\frac{1}{4}x$

Second equation: $12y = -3x$
$y = -\frac{3}{12}x = -\frac{1}{4}x$

Step2: Analyze the equations

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

Step3: Find solution set

All points on the line satisfy both equations, so there are infinitely many solutions.

Answer:

The system has infinitely many solutions, represented by all points on the line $y = -\frac{1}{4}x$ (or $x + 4y = 0$).