Question 381352: Could someone please help? I need to graph a system of linear inequalities, then test to see what satisfies both. Here is the system:
x+y>4
x+y<-1
Here's what I have done so far:
For Line 1, the first inequality:
x-intercept is (4,0) and y-intercept is (0,4)
For Line 2, the second inequality:
x-intercept is (-1,0) and y-intercept is (0,-1).
Ok, both these lines are dashed lines, since neither are equal, and therefore included, so I end up with two parallel dashed lines. My problem: I can't find an answer to satisfy BOTH inequalities, so I don't know what to shade in as "true".
Can someone please set me straight and tell me what I am doing wrong? Thank you!!!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Consider this: Let z=x+y be some number
So the system
x+y>4
x+y<-1
is really saying
z > 4
z < -1
So the question is now: what number (z) is BOTH greater than 4 AND less than -1? This is impossible. Since no number exists, this means that there are no solutions to the system of inequalities above.
So there are no solutions to the system
x+y>4
x+y<-1
Visually, you'll get the following
Where the blue shaded region refers to the solution set of x+y>4 and the red shaded region refers to the solution set of x+y<-1. Since the two regions will NEVER intersect (at any point in the xy plane), this means that the solution set is empty.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my tutoring website
Jim
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! x+y>4
x+y<-1
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Graph both boundary lines as dashed lines:
y = -x+4
y = -x-1
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Since you want y > -x+4, shade the half-plane ABOVE the boundary line.
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Since you want y < -x-1, shade the half-plane BELOW the boundary line.
----
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Since there are no points which satisfy both conditions there
is no solution for the system.
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Cheers,
Stan H.
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