Question

choose the graph that matches the following system of equations:
$x - 3y = -12$
$2x - y = 1$

Explanation:

Step1: Rewrite equations to slope-intercept form

For $x - 3y = -12$:

$$\begin{align*} -3y &= -x -12\\ y &= \frac{1}{3}x + 4 \end{align*}$$

For $2x - y = 1$:

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

Step2: Identify key line features

Line 1 ($y=\frac{1}{3}x + 4$): Positive slope ($\frac{1}{3}$), y-intercept $(0,4)$
Line 2 ($y=2x -1$): Positive slope ($2$), y-intercept $(0,-1)$

Step3: Match to correct graph

Only the second graph has one line with a gentle positive slope (crossing y-axis at 4) and one steep positive slope (crossing y-axis at -1).

Answer:

The second graph (middle top option, with one line crossing y-axis at 4 and the other crossing y-axis at -1, both with positive slopes)