Questions: Graph the solution set of the system of inequalities. x=y ≤ 2 x ≥ 2

Graph the solution set of the system of inequalities. x=y ≤ 2 x ≥ 2
Transcript text: Graph the solution set of the system of inequalities. \[ \begin{array}{l} x=y \leqslant 2 \\ x \geq 2 \end{array} \]
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Solution

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Solution Steps

Step 1: Graph x = 2

Draw a vertical line at x = 2. Since the inequality is x ≥ 2, shade the region to the right of the line. The line should be solid because the inequality includes the equal sign.

Step 2: Graph y ≤ 2

Draw a horizontal line at y = 2. Since the inequality is y ≤ 2, shade the region below the line. The line should be solid because the inequality includes the equal sign.

Step 3: Find the overlapping region

The solution to the system of inequalities is the region where both shaded areas overlap. This will be the region to the right of the vertical line x=2 and below the horizontal line y=2, including the lines themselves.

Final Answer

The graph should show two solid lines, one vertical at x=2 and one horizontal at y=2. The overlapping shaded region will be to the right of x=2 and below y=2.

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