Questions: Click on each graph to enlarge it. Find the coordinate plane that represents the solution of this system. y < -x + 3 y - 1 ≥ x Click on the correct answer. graph 1 graph 2 graph 3

Solution Steps

The first inequality is $y < -x + 3$. The corresponding equality $y = -x + 3$ is a line with a y-intercept of 3 and a slope of -1. Since the inequality is strictly less than, the line should be dashed. The region below the line is shaded.

The second inequality is $y - 1 \ge x$, which can be rewritten as $y \ge x + 1$. The corresponding equality $y = x + 1$ is a line with a y-intercept of 1 and a slope of 1. Since the inequality is greater than or equal to, the line should be solid. The region above the line is shaded.

The solution to the system of inequalities is the intersection of the shaded regions of the two inequalities. Graph 2 correctly shows a dashed line with a negative slope and a y-intercept of 3 shaded below, and a solid line with a positive slope and a y-intercept of 1 shaded above. The intersection of these shaded regions is correctly represented in Graph 2.

Final Answer