SOlve the system of inequalites by graphing.
y< -4x-2
-
y >3x-3
Let's use Wolfram great website ....
http://www.wolframalpha.com/input/?i=plot+y%3D+-4x-2+%3B+y%3D3x-3
shade in the region BELOW the blue line
shade in the region ABOVE the red line
your graph will be the region belonging to both shaded parts.
Draw a dotted line for the boundaries, since the points on the lines are excluded.
To solve the system of inequalities by graphing, follow these steps:
1. Graph the first inequality, y < -4x - 2:
- Start by graphing the related equation, y = -4x - 2, which is a straight line.
- To graph it, plot two points that satisfy the equation. For example, when x = 0, y = -2, so plot the point (0, -2). When x = 1, y = -6, so plot the point (1, -6).
- Connect the two points with a straight line.
2. Shade the region below the line:
- Since the inequality is y < -4x - 2, the region below the line represents all the possible solutions.
- Shade the area below the line to indicate this.
3. Graph the second inequality, y > 3x - 3:
- Just like with the first inequality, start by graphing the related equation, y = 3x - 3.
- Plot two points that satisfy the equation. For example, when x = 0, y = -3, so plot the point (0, -3). When x = 1, y = 0, so plot the point (1, 0).
- Connect the two points with a straight line.
4. Shade the region above the line:
- Since the inequality is y > 3x - 3, the region above the line represents all the possible solutions.
- Shade the area above the line to indicate this.
5. Analyze the overlapping shaded areas:
- The overlapping region between the two shaded areas represents the solutions that satisfy both inequalities.
- Identify the common shaded area and observe its shape and position.
By following these steps, you will have graphically solved the system of inequalities.