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Graph the system of inequalities (y>−3),(y<−∣x+2∣). Which two quadrants does the solution lie in?

a) Quadrants 2 and 3
b) Quadrants 1 and 2
c) Quadrants 3 and 4
d) Quadrants 1 and 4

User Quazgar
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1 Answer

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Final answer:

The solution to the system of inequalities lies in Quadrants 3 and 4.

Step-by-step explanation:

To graph the system of inequalities: y > -3 and y < -|x+2|, we need to graph the two individual inequalities.

The inequality y > -3 represents a horizontal line parallel to the x-axis at y = -3. Since y is greater than -3, the solution lies above this line, in the upper half of the coordinate plane.

The inequality y < -|x+2| represents a V-shaped graph opening downward. The vertex of the V is located at (-2, 0) and the V opens downwards because of the negative sign in front of the absolute value. Since y is less than -|x+2|, the solution lies below this V-shaped graph, in the lower half of the coordinate plane.

Therefore, the solution to the system of inequalities lies in Quadrants 3 and 4.

User Hermiod
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