Question

by inspecting the graph, what can you determine about the solution(s) of this system? the system of equations has

Explanation:

Step1: Analyze the equations' slopes

First, rewrite the equations in slope - intercept form ($y = mx + b$, where $m$ is the slope and $b$ is the y - intercept).

For the first equation $6y=-4x + 24$, divide both sides by 6:
$y=\frac{-4}{6}x+\frac{24}{6}=-\frac{2}{3}x + 4$

For the second equation $18y=-12x + 72$, divide both sides by 18:
$y=\frac{-12}{18}x+\frac{72}{18}=-\frac{2}{3}x + 4$

Step2: Determine the relationship between the lines

Since both equations have the same slope ($m =-\frac{2}{3}$) and the same y - intercept ($b = 4$), the two lines are coincident (they are the same line).

Step3: Determine the number of solutions

When two lines are coincident, every point on the line is a solution to the system of equations. So the system of equations has infinitely many solutions.

Answer:

infinitely many solutions