Match each system of inequalities with the correct graph from choices A–D. x ≥ 5 y ≤ -3

Verified step by step guidance

1. Step 1: Understand the inequalities given: \(x \geq 5\) means the solution includes all points to the right of and on the vertical line \(x=5\). \(y \leq -3\) means the solution includes all points below and on the horizontal line \(y=-3\).
2. Step 2: Identify the boundary lines on the graphs. The vertical line at \(x=5\) should be solid (because of the \geq sign) and the shading should be to the right of this line.
3. Step 3: The horizontal line at \(y=-3\) should also be solid (because of the \leq sign) and the shading should be below this line.
4. Step 4: Look for the graph where the shaded region is the intersection of the two conditions: to the right of \(x=5\) and below \(y=-3\). This means the shaded area should be in the lower right quadrant formed by these two lines.
5. Step 5: Match this description to the correct graph choice. The graph that shows shading to the right of \(x=5\) and below \(y=-3\) with solid boundary lines is the correct match.

Key Concepts

Graphing Linear Inequalities

Graphing linear inequalities involves shading the region of the coordinate plane that satisfies the inequality. For example, x ≥ 5 means shading all points to the right of the vertical line x = 5, including the line itself if it is solid.

Interpreting Boundary Lines

The boundary line of an inequality is drawn as solid if the inequality includes equality (≥ or ≤) and dashed if it does not (> or <). This line divides the plane into two halves, one of which satisfies the inequality.

Combining Systems of Inequalities

When dealing with a system of inequalities, the solution is the intersection of the shaded regions for each inequality. For x ≥ 5 and y ≤ -3, the solution is where the shaded region to the right of x=5 overlaps with the shaded region below y=-3.