Question

⑤ $2x - y \geq -6$
$x > 2$

Explanation:

Step1: Rewrite first inequality to slope-intercept form

Rearrange $2x - y \geq -6$ to solve for $y$:
$y \leq 2x + 6$

Step2: Identify boundary lines

• For $y \leq 2x + 6$: Boundary is $y=2x+6$ (solid line, since $\geq$ includes equality).
• For $x > 2$: Boundary is $x=2$ (dashed line, since $>$ excludes equality).

Step3: Test points for shading

• For $y \leq 2x + 6$: Test $(0,0)$: $0 \leq 0 + 6$ is true, shade below the solid line.
• For $x > 2$: Shade all regions where $x$ is greater than 2 (right of dashed $x=2$).

Step4: Find overlapping shaded region

The solution is the area that is both below $y=2x+6$ (solid line) and right of $x=2$ (dashed line).

Answer:

The solution is the overlapping shaded region:

1. Draw a solid line for $y=2x+6$ (passes through $(0,6)$ and $(-3,0)$), shade below this line.
2. Draw a dashed vertical line at $x=2$, shade to the right of this line.
3. The intersection of these two shaded areas is the solution set.