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

Choose the graph that matches the following system of equations:

x-3y=-12
2x-y=1
Transcript text: Choose the graph that matches the following system of equations: \[ \begin{array}{l} x-3 y=-12 \\ 2 x-y=1 \end{array} \]
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Solution

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Solution Steps

Step 1: Rewrite the equations in slope-intercept form.

The first equation, x - 3y = -12 can be rewritten as: -3y = -x - 12 y = (1/3)x + 4

The second equation, 2x - y = 1 can be rewritten as: -y = -2x + 1 y = 2x - 1

Step 2: Identify the slope and y-intercept of each equation.

For the first equation, y = (1/3)x + 4, the slope is 1/3 and the y-intercept is 4.

For the second equation, y = 2x - 1, the slope is 2 and the y-intercept is -1.

Step 3: Compare the graphs with the equations.

The first graph shows lines that roughly correspond to the calculated slopes and y-intercepts. The red line has a positive y-intercept around 4 and shallow positive slope, while the blue line has a negative y-intercept close to -1 and a steeper positive slope. The second graph doesn't match.

Final Answer The first graph.

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