Solve the system of inequalities by graphing. What are the coordinates?
y < 2x + 3
2x - y <= 4
To solve the system of inequalities by graphing, we first need to graph each inequality separately and then find the coordinates where the graphs intersect.
For the first inequality, y < 2x + 3, we can start by graphing the line y = 2x + 3. To do this, we can plot a few points on the line and connect them.
When x = 0, y = 2(0) + 3 = 3. So one point on the line is (0, 3).
When x = 1, y = 2(1) + 3 = 5. Another point on the line is (1, 5).
Plot these two points and connect them with a straight line.
Now, to determine which region of the graph to shade, we need to test a point that is not on the line. Let's test the point (0, 0).
When we substitute x = 0 and y = 0 into the inequality y < 2x + 3, we get 0 < 2(0) + 3, which simplifies to 0 < 3. Since this statement is true, we shade the region below the line y = 2x + 3.
Now, let's graph the second inequality, 2x - y <= 4. We can start by graphing the line 2x - y = 4.
To graph this line, we can pick two arbitrary x-values and solve for y. For example, when x = 0, we have -y = 4, so y = -4. This gives us the point (0, -4).
When x = 1, we have 2(1) - y = 4, which simplifies to -y = 2, and y = -2. This gives us the point (1, -2).
Plot these two points and connect them with a straight line.
Now, to determine which region of the graph to shade, we need to test a point that is not on the line. Let's test the point (0, 0).
When we substitute x = 0 and y = 0 into the inequality 2x - y <= 4, we get 2(0) - 0 <= 4, which simplifies to 0 <= 4. Since this statement is true, we shade the region below the line 2x - y = 4.
Now, we need to find the coordinates where the two shaded regions intersect. By inspecting the graph, we can see that the intersection point is approximately (2, 7).
So, the coordinates where the two graphs intersect are (2, 7).