Question

Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3

Answer 1

First solve for y in $2x - 3y \le 12$ to get $y \ge \frac{2}{3}x-4$. The inequality sign flips because we divided both sides by a negative value.

To graph $y \ge \frac{2}{3}x-4$ we need to graph the boundary line y = (2/3)x - 4. This line has a y intercept of (0,-4) and another point on the line is (6,0).

Draw a solid line through (0,-4) and (6,0). The boundary line is solid because of the "or equal to" part of the inequality sign. The last part is to shade above the boundary line because of the "greater than" sign in $y \ge \frac{2}{3}x-4$.

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As for graphing y < -3, we draw a horizontal dashed line through -3 on the y axis. The line is dashed because there is no "or equal to" here. We do not include boundary points as part of the solution set. Shade below this dashed line due to the "less than" sign.

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After doing both of these things on the same xy grid, you'll get something that looks like choice C. I'm assuming choice C has a dashed line for the red region.

Answer: Choice C

Answer 2

The graph is image 2. (last option)

We first draw the lines 2x - 3y = 12 and y=-3. Image 1.

For 2x - 3y ≤ 12

or, 2x - 12 ≤ 3y

or, 3y ≥ 2x - 12

or, y ≥ (2x - 12)/3

we shade upwards.

For y < - 3 we shade below.

So the graph is image 2.

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