Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y > 2x + 4
x + y ≤ 6
To graph the system of inequalities, follow these steps:
First, let's graph the inequality y > 2x + 4:
1. Start by graphing the equation y = 2x + 4, which is the line that represents y = 2x + 4.
2. Choose any point not on the line and test it in the inequality. For simplicity, let's choose the point (0, 0). Substitute the x and y values into the inequality: 0 > 2(0) + 4, which simplifies to 0 > 4. Since this is false, the point (0, 0) is not part of the solution. Therefore, shade the region above the line.
Now, let's graph the inequality x + y ≤ 6:
1. Start by graphing the equation x + y = 6, which is the line that represents x + y = 6.
2. Choose any point not on the line and test it in the inequality. For simplicity, let's choose the point (0, 0). Substitute the x and y values into the inequality: 0 + 0 ≤ 6, which simplifies to 0 ≤ 6. Since this is true, the point (0, 0) is part of the solution. Therefore, shade the region below the line.
The shaded regions for each inequality should overlap, representing the solution to the system of inequalities.