Graph the system of inequalities then substitute the (x,y)order pair into both inequalities.
y>3x+1
y<-2/3x+4
(second one has a line under the arrow)
I don't get what they are asking for? if they want me to solve it how am I suppose to set it up?
You know how to graph the line
y = 3x+1
y > 3x+1 is everything where y is above the line.
Similarly, y <= -2/3 x + 4
is everything below that line, and including the line itself.
Take a trip to wolframalpha.com and enter
solve y > 3x + 1, y <= -2/3 x + 4
It will graph the region in blue which is above one line and below the other.
To graph the system of inequalities, you need to first plot the boundary lines for each inequality and then shade the appropriate regions based on the given inequalities.
1. Graphing the first inequality:
Start by graphing the boundary line y = 3x + 1. To do this, you can plot two points on the line and then draw a straight line through them. For example, when x = 0, y = 1, and when x = 1, y = 4. Plotting these two points and drawing a line through them gives you the boundary line for the first inequality.
2. Graphing the second inequality:
For the second inequality y < -2/3x + 4, notice that there is a line under the arrow, indicating that the boundary line should be dashed. Follow the same process as before to graph the boundary line y = -2/3x + 4. Plot two points on the line, and draw a dashed line through them.
3. Shading the appropriate regions:
To determine which side of each boundary line to shade, you need to choose a test point that is not on the line. The origin (0,0) is generally a convenient test point to use. Substitute the coordinates of the test point into each inequality and check if the resulting inequalities are true or false.
- Substitute (0,0) into the first inequality:
y > 3x + 1
0 > 3(0) + 1
0 > 1
The inequality is false, so you do not shade the side where the origin is located.
- Substitute (0,0) into the second inequality:
y < -2/3x + 4
0 < -2/3(0) + 4
0 < 4
The inequality is true, so you shade the side where the origin is located.
After shading the appropriate regions based on the test points, you will have the graph of the system of inequalities. The shaded region where the second inequality is true and the first inequality is false represents the solution to the system.