SOLUTION: Show graphically the solution set for the linear inequalities. x + y ≤ 4 2x - y ≤ 4 Plot the graph of the function

Algebra ->  Graphs -> SOLUTION: Show graphically the solution set for the linear inequalities. x + y ≤ 4 2x - y ≤ 4 Plot the graph of the function       Log On


   

Question 1153833: Show graphically the solution set for the linear inequalities.
x + y ≤ 4
2x - y ≤ 4
Plot the graph of the function

Found 3 solutions by josgarithmetic, MathLover1, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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Show graphically the solution set for the linear inequalities.
x + y ≤ 4
2x - y ≤ 4
Plot the graph of the function
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What function?

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Your first inequality is also y%3C=-x%2B4. Shade below and including the line.
Your second inequality is also y%3E=2x-4. Shade above and including the line.

The doubly-shaded region is the solution for the inequality system.
---
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The given system represents TWO linear functions. The graph has now been adequately shown.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+y+%3C=+4
2x+-+y+%3C=+4
graph both as a lines
x+%2B+y+=+4=>y+=-x%2B+4
2x+-+y+=+4=>y+=2x-4
you need two points for each line to draw

y+=-x%2B+4
if x=0=>y=4=>(0,4)
if y=0=>x=4=>(4,0)

y+=2x-4
if x=0=>y=-4=>(0,-4)
if y=0=>x=2=>(2,0)

graph:
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B+4%2C+2x-4%29+
since you have the linear inequalities
x+%2B+y+%3C=+4=>+y+%3C=+-x%2B4-> shade the part below the line
2x+-+y+%3C=+4=>2x+-+4+%3C=+y =>y%3E=2x+-+4+ > shade the part above the line
solution part is that triangle with base on y-axis, and shaded part looks like this:


View post on imgur.com

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x+%2B+y+%3C=+4%2C%0D%0A2x+-+y+%3C=+4%29

First graph the boundary lines, one at a time, which are the lines whose
equations are just like the inequalities with the symbols of inequality changed
to symbols of equality ("=").

system%28x+%2B+y+=+4%2C%0D%0A2x+-+y+=+4%29

We graph the first boundary line (in green), x + y = 4, which has intercepts
(0,4) and (4,0)

 


Before we draw the other boundary line, let's find out which side of the line
all the solutions to the inequality x + y ≤ 4 are on.  We do that by
substituting any point that isn't on the line into the inequality as a test
point.  The easiest test point to substitute is the origin (0,0).  We can use
it as a test point because (0,0) doesn't lie on the line.  Substituting
(x,y) = (0,0)

x + y ≤ 4
0 + 0 ≤ 4
    0 ≤ 4   <--- this is true so the solutions lie on the side of the line which
the test point (0,0), the origin, lies on, which is BELOW and to the LEFT of the
green line.

Next we graph the second boundary line (in blue), 2x - y = 4, which has
intercepts (0,-4) and (2,0)

 

Let's find out which side of the line all the solutions to the inequality
2x - y ≤ 4 are on.  Again we do that by substituting any point that isn't on the
line into the inequality as a test point.  The easiest test point to substitute,
again,  is the origin (0,0).  We can use it again as a test point because (0,0)
doesn't lie on the line.  Substituting

(x,y) = (0,0)

  2x - y ≤ 4
2(0) + 0 ≤ 4
       0 ≤ 4   <--- this is true so the solutions lie on the side of the line which
the test point (0,0), the origin, lies on, which is ABOVE and to the LEFT of the
blue line.

So finally we shade the area which is BELOW and to the LEFT of the
green line AND which is ABOVE and to the LEFT of the blue line.




Edwin