Question

1. graph the system of equations and determine the solution. 6x - 3y = 3 4x - 2y = 8

Explanation:

Step1: Rewrite to slope-intercept form

For $6x-3y=3$:

$$\begin{align*} -3y&=-6x+3\\ y&=2x-1 \end{align*}$$

For $4x-2y=8$:

$$\begin{align*} -2y&=-4x+8\\ y&=2x-4 \end{align*}$$

Step2: Analyze line properties

Both lines have slope $m=2$, so they are parallel. Their y-intercepts are $b_1=-1$ and $b_2=-4$, so they are distinct parallel lines.

Step3: Determine solution type

Parallel distinct lines never intersect, so there is no solution to the system.

Answer:

There is no solution to the system, as the two lines are parallel and never intersect.