Questions: Graph the solution to the following system of inequalities. y < -5x + 2 y > 2x - 9

Solution Steps

To graph $y < -5x + 2$, first graph the line $y = -5x + 2$. This line has a y-intercept of 2 and a slope of -5. Since the inequality is strictly less than, the line should be dashed. Shade the region below the line because $y$ is less than the expression.

To graph $y > 2x - 9$, first graph the line $y = 2x - 9$. This line has a y-intercept of -9 and a slope of 2. Since the inequality is strictly greater than, the line should be dashed. Shade the region above the line because $y$ is greater than the expression.

The solution to the system of inequalities is the region where the shading from both inequalities overlaps.

Final Answer: The solution is the overlapping shaded region. The lines themselves are not included in the solution because both inequalities use $\lt$ and $\gt$ and not $\le$ and $\ge$.