Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}x > -3 \\\\ y \\geq 6\\end{cases}$$

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step 3 of 3 : graph the solution set for the system.\
answer

Explanation:

Step1: Graph boundary $x=-3$

Draw a dashed vertical line at $x=-3$ (dashed because the inequality is $x > -3$, so the line itself is not part of the solution). Shade the region to the right of this line, since $x$ values greater than $-3$ lie here.

Step2: Graph boundary $y=6$

Draw a solid horizontal line at $y=6$ (solid because the inequality is $y \geq 6$, so the line is part of the solution). Shade the region above this line, since $y$ values greater than or equal to 6 lie here.

Step3: Identify overlapping region

The solution set is the intersection of the two shaded regions: the area that is both to the right of $x=-3$ and above or on $y=6$.

Answer:

The solution is the region bounded by the dashed vertical line $x=-3$ (not included) and the solid horizontal line $y=6$ (included), covering all points where $x > -3$ and $y \geq 6$. Visually, this is the top-right quadrant relative to the intersection point $(-3, 6)$.