Question

1. $y = \frac{3}{2}x - 1$

$-6x + 4y = -12$

Explanation:

Step1: Rewrite 2nd equation to slope-intercept form

Start with $-6x + 4y = -12$. Isolate $4y$:
$4y = 6x - 12$
Divide by 4:
$y = \frac{6}{4}x - \frac{12}{4}$
Simplify:
$y = \frac{3}{2}x - 3$

Step2: Compare slopes and y-intercepts

First equation: $y = \frac{3}{2}x - 1$ (slope $m=\frac{3}{2}$, y-intercept $b=-1$)
Second equation: $y = \frac{3}{2}x - 3$ (slope $m=\frac{3}{2}$, y-intercept $b=-3$)

Step3: Analyze the system

Equal slopes ($\frac{3}{2}$) and different y-intercepts mean the lines are parallel and never intersect. Thus, there is no solution to the system.

Answer:

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