SOLUTION: I still haven't received an answer and I have class tomorrow. Could someone please help me with graphing this equation?
What does the region look like and how do I graph it?
Algebra.Com
Question 139531This question is from textbook Essentials of College Mathematics
: I still haven't received an answer and I have class tomorrow. Could someone please help me with graphing this equation?
What does the region look like and how do I graph it?
4x+3y=>24
3x+4y=>8
x=>0
y=>0
I would appreciate your help as soon as possible.
Anne
This question is from textbook Essentials of College Mathematics
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of inequalities
In order to graph this system of inequalities, we need to graph each inequality one at a time.
First lets graph the first inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver)
graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point
Substitute (0,0) into the inequality
Plug in and
Simplify
(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)
Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of with the boundary (which is the line in red) and the shaded region (in green)
---------------------------------------------------------------
Now lets graph the second inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver)
graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point
Substitute (0,0) into the inequality
Plug in and
Simplify
Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of with the boundary (which is the line in red) and the shaded region (in green)
---------------------------------------------------------------
Now lets graph the third inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (simply draw a vertical line through )
graph of (note:the graph is the line that is overlapping the y-axis. So it may be hard to see)
Now lets pick a test point, say (1,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point
Substitute (1,0) into the inequality
Plug in and
Simplify
Since this inequality is true, we simply shade the entire region that contains (1,0)
Graph of with the boundary (which is the line in red) and the shaded region (in green)
---------------------------------------------------------------
Now lets graph the fourth inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (simply draw a horizontal line through )
graph of (note:the graph is the line that is overlapping the x-axis. So it may be hard to see)
Now lets pick a test point, say (0,1). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point
Substitute (0,1) into the inequality
Plug in and
Simplify
Since this inequality is true, we simply shade the entire region that contains (0,1)
Graph of with the boundary (which is the line in red) and the shaded region (in green)
---------------------------------------------------------------
So we essentially have these 4 regions:
Region #1
Graph of
Region #2
Graph of
Region #3
Graph of
Region #4
Graph of
When these inequalities are graphed on the same coordinate system, the regions overlap to produce this region. It's a little hard to see, but after evenly shading each region, the intersecting region will be the most shaded in.
Here is a cleaner look at the intersection of regions
Here is the intersection of the 4 regions represented by the series of dots
RELATED QUESTIONS
I have an quadratic equation that has to do with graphing and its due tomorrow night... (answered by Edwin McCravy)
Can someone please help me with this question...i have a test tomorrow and I dont know... (answered by mananth)
I'm doing a math final that needs to be passed in tomorrow. I really needed to pass this... (answered by Alan3354,MathTherapy)
6x-7= 2x=29 My teach helped me to understand this. I got an answer of x=9. My teacher... (answered by CassieLynn,stanbon,ankor@dixie-net.com,josmiceli)
I could really use this some help with this logarithm problem. I have submitted this... (answered by chriswen,josmiceli)
I would like if someone could help me with this problem.
Find the measure of angle T (answered by doukungfoo)
How would you write the following expression with a rational denominator and in simplest... (answered by nerdybill)
Could someone please help me solve and graph the following equation?
I have tried to... (answered by josmiceli)
I have an quadratic equation that has to do with graphing and its due tomorrow night... (answered by nerdybill)