Questions: Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y > (3/2) x - 6 y <= -x - 1

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y > (3/2) x - 6 y <= -x - 1
Transcript text: Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. \[ \begin{array}{l} y>\frac{3}{2} x-6 \\ y \leq-x-1 \end{array} \]
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Solution

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Solution Steps

Step 1: Graph the first inequality

The inequality y > (3/2)x - 6 is graphed with a dashed line because the inequality is strictly greater than. The line has a y-intercept of -6 and a slope of 3/2. Shade the region above the line since it is y _greater than_.

Step 2: Graph the second inequality

The inequality y ≤ -x - 1 is graphed with a solid line because the inequality includes "less than or equal to". The line has a y-intercept of -1 and a slope of -1. Shade the region below the line because it is _less than or equal to_.

Step 3: Identify the solution set and a point within it

The solution set is the region where the shading for both inequalities overlaps. One point in this solution set is (0, -2).

Final Answer:

The graph of the system of inequalities shows the overlapping shaded region as the solution set. One point within the solution set is (0, -2).

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