Question

written assignme
answer each of the following questions completely. show
points are rewarded based on proper steps/work performe
using appropriate mathematical notation) and correct answ
possible in the assignment.

1. (3 points each) solve each system by graphing:

$2x = 3y + 3$
$3y = 2x + 9$

Explanation:

Step1: Rewrite in slope-intercept form

First equation:
$2x = 3y + 3$
$3y = 2x - 3$
$y = \frac{2}{3}x - 1$

Second equation:
$3y = 2x + 9$
$y = \frac{2}{3}x + 3$

Step2: Analyze slopes and intercepts

Both lines have slope $\frac{2}{3}$, so they are parallel. The y-intercepts are $-1$ and $3$, so the lines never intersect.

Step3: Verify via graphing

Plot $y = \frac{2}{3}x - 1$ (passes through $(0,-1)$ and $(3,1)$) and $y = \frac{2}{3}x + 3$ (passes through $(0,3)$ and $(3,5)$). The lines are parallel with no overlap.

Answer:

The system has no solution (inconsistent system, parallel lines).