Question

graph the system of equations, and determine the solutio
$y = -dfrac{3}{4}x + 2$
$4y = -3x + 12$
use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Rewrite second equation to slope-intercept form

Divide both sides of $4y=-3x+12$ by 4:
$\frac{4y}{4}=\frac{-3x+12}{4}$
Simplify to get $y=-\frac{3}{4}x+3$

Step2: Compare the two equations

First equation: $y=-\frac{3}{4}x+2$
Second equation: $y=-\frac{3}{4}x+3$
Both have the same slope $m=-\frac{3}{4}$ but different y-intercepts (2 vs. 3).

Step3: Analyze graph and solution

Parallel lines (same slope, different intercepts) never intersect, so there is no solution to the system.

Answer:

The system has no solution, as the two lines are parallel and never intersect.