Graph the solution set of the following system of inequalities. \[ \begin{array}{l}y>-2 x+4 \\ y

To graph the solution set of the system of inequalities given by: 1. \( y > -2x + 4 \) 2. \( y < x - 4 \) we can follow these steps: ### Step 1: Graph the boundary lines 1. **For the first inequality \( y > -2x + 4 \)**: - The boundary line is \( y = -2x + 4 \). - This line has a y-intercept of 4 and a slope of -2. - To graph it, plot the y-intercept (0, 4) and another point using the slope. For example, if \( x = 2 \), then \( y = -2(2) + 4 = 0 \), giving the point (2, 0). - Draw a dashed line for \( y = -2x + 4 \) because the inequality is strict (greater than, not greater than or equal to). 2. **For the second inequality \( y < x - 4 \)**: - The boundary line is \( y = x - 4 \). - This line has a y-intercept of -4 and a slope of 1. - To graph it, plot the y-intercept (0, -4) and another point using the slope. For example, if \( x = 4 \), then \( y = 4 - 4 = 0 \), giving the point (4, 0). - Draw a dashed line for \( y = x - 4 \) because the inequality is strict (less than, not less than or equal to). ### Step 2: Shade the appropriate regions 1. **For \( y > -2x + 4 \)**: - Shade the region above the line \( y = -2x + 4 \). 2. **For \( y < x - 4 \)**: - Shade the region below the line \( y = x - 4 \). ### Step 3: Identify the solution set The solution set is the region where the shaded areas of both inequalities overlap. ### Final Graph You can use graphing software or graph paper to plot these lines and shade the appropriate regions. The overlapping shaded area represents the solution set for the system of inequalities. If you have access to a graphing tool, you can input the inequalities directly to visualize the solution set.