Question

Graph the solution set of each system of inequalities. x + y ≥ 0 2x - y ≥ 3

Accepted Answer

Step 1: Understand the system of inequalities. You are given two inequalities: $$x - y \geq 0$$ and $$4x + 5y \geq 9. $$Your goal is to graph the solution set that satisfies both inequalities simultaneously. Step 2: Rewrite each inequality in slope-intercept form ($$y = mx + b) to $$make graphing easier. For the first inequality, $$x - y \geq 0$$, rearrange to isolate $$y$$: $$-y \geq -x$$ which simplifies to $$y \leq x$$ after multiplying both sides by $$-1$$ and reversing the inequality sign. Step 3: For the second inequality, $$4x + 5y \geq 9$$, isolate $$y$$: $$5y \geq 9 - 4x$$, then divide both sides by 5 to get $$y \geq \frac{9}{5} - \frac{4}{5}x. $$Step 4: Graph the boundary lines $$y = x$$ and $$y = \frac{9}{5} - \frac{4}{5}x. $$Use a solid line for each because the inequalities include equality (\geq or \leq). Step 5: Determine the solution regions for each inequality by testing points on either side of the boundary lines. For $$y \leq x$$, shade the region below or on the line $$y = x. $$For $$y \geq \frac{9}{5} - \frac{4}{5}x$$, shade the region above or on the line $$y = \frac{9}{5} - \frac{4}{5}x. $$The solution set is the intersection of these shaded regions.

Graph the solution set of each system of inequalities.
x + y ≥ 0
2x - y ≥ 3

Verified video answer for a similar problem:

Key Concepts

Graphing Linear Inequalities

System of Inequalities

Testing Points to Determine Solution Regions