Graph the system of inequalities:

\[ y < 2x + 2 \]

\[ y \geq -x - 1 \]

To graph the system of inequalities you have to start with drawing both lines:

y=2x+2: this one is crossing points: (0,2) and (-1,0)
y=-x-1: this one is crossing: (0,-1) and (-1,0)

When you have it done you have to identify the area (set of points)** that satisfies both inequalities**. In the first case: y<2x+2, these gonna be all points below this line excluding the line (because the sign is "<"). In the second case: y > -x-1, the area includes all the points above this line including the line (because the sign is " > ").
The result is a common set of the areas: x>-1 and -x-1<y<2x+2.
Please find the graph attached!
Hope it helps!

Answered by voytek | 2024-06-10

To graph the system of inequalities, first draw the lines for both inequalities. The region below the dashed line from y < 2 x + 2 and above the solid line from y ≥ − x − 1 represents the solution. The overlapping shaded area is the set of points that satisfies both inequalities.
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Answered by voytek | 2024-12-23