Question

graph and determine the solution of the system of equations.
$x + 3y = 0$
$9y = -3x$
use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Rewrite first equation to slope-intercept form

Solve $x + 3y = 0$ for $y$:
$3y = -x$
$y = -\frac{1}{3}x$

Step2: Rewrite second equation to slope-intercept form

Solve $9y = -3x$ for $y$:
$y = -\frac{3}{9}x = -\frac{1}{3}x$

Step3: Analyze the two equations

Both equations simplify to the same linear equation $y = -\frac{1}{3}x$, meaning they represent the same line.

Answer:

All points on the line $y = -\frac{1}{3}x$ are solutions; the system has infinitely many solutions. To graph, plot points such as $(0,0)$, $(3,-1)$, $(-3,1)$ and draw a straight line through them.