Question

1. \

$$\begin{cases} 3y = 4x - 6 \\\\ 8x - 6y = -30 \\end{cases}$$

Explanation:

Step1: Rewrite equations to slope-intercept form

First equation: $3y=4x-6$ → $y=\frac{4}{3}x-2$
Second equation: $8x-6y=-30$ → $-6y=-8x-30$ → $y=\frac{4}{3}x+5$

Step2: Analyze slopes and intercepts

Both lines have slope $\frac{4}{3}$ (parallel), with different y-intercepts ($-2$ and $5$). Parallel lines never intersect, so no solution exists.

Answer:

There is no solution (the system is inconsistent, as the lines are parallel and never meet).