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Graph the solution to the following system of inequalities.
-5x+6y≥18
x> -2
y≤7

1 Answer

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Final answer:

To graph the solution to the system of inequalities, graph each inequality separately and shade the region that satisfies both inequalities.

Step-by-step explanation:

To graph the solution to the system of inequalities, we need to graph each inequality separately and shade the region that satisfies both inequalities. Let's start with the first inequality, -5x + 6y ≥ 18:

Step 1: Rewrite the inequality in slope-intercept form (y = mx + b) by solving for y:

y ≥ (5/6)x + 3

Step 2: Graph the boundary line y = (5/6)x + 3 as a solid line (since it is ≥ and not >).

Step 3: Shade the region above the line, including the line itself, since y is greater than or equal to (5/6)x + 3.

Next, let's graph the second inequality, x > -2:

Step 1: Graph the vertical line x = -2 as a dashed line (since it is > and not ≥).

Step 2: Shade the region to the right of the line, excluding the line itself, since x is greater than -2.

The shaded region that satisfies both inequalities is the solution to the system of inequalities.

User Richard Dunn
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