Systems of Inequalities — Quiz

Question 2 • Algebra 2

Which graph represents the solution of x squared plus y squared is less than 25 and y squared is less than 6 x ?

Answer

Image with description On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything outside of the circle and outside of the parabola is shaded.

Image with description On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything inside of the circle and outside of the parabola is shaded.

Image with description On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything inside of the circle and inside of the parabola is shaded.

Explanation

The inequality x² + y² < 25 describes points inside the circle of radius 5 centered at (0, 0). The inequality y² < 6x is equivalent to x > y²/6, so it describes the region to the right of the parabola, inside its opening. The overlap is inside the circle and inside the parabola, which is choice A.

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