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If the system of inequalities $$y \geq 2x + 1$$ and $$y > \frac{1}{2}x - 1$$ ...

Question

If the system of inequalities $$y \geq 2x + 1$$ and $$y > \frac{1}{2}x - 1$$ is graphed in the xy-plane above, which quadrant contains no solutions to the system?

Options

A)
B)
C)
D)
There are solutions in all four quadrants.

Choice C is correct. To determine which quadrant does not contain any solutions to the system of inequalities, graph the inequalities. Graph the inequality y $$\geq$$ 2x + 1 by drawing a line through the y-intercept (0, 1) and the point (1, 3), as shown. The solutions to this inequality are all points contained on and above this line. Graph the inequality y > $$\frac{1}{2}$$x - 1 by drawing a dashed line through the y-intercept (0, -1) and the point (2, 0), as shown. The solutions to this inequality are all points above this dashed line.