SOLUTION: solve the following system of linear inequalities by graphing. x-2y<=4, x>1

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Question 82620: solve the following system of linear inequalities by graphing. x-2y<=4, x>1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for y in x-2y%3C=4
-2y%3C=4-x Subtract x from both sides
y%3E=%281%2F2%29x-2 Divide both sides by -2

So the graph will have the equations x=1(which will be a dashed line) and y=%281%2F2%29x-2 (just replace the inequality signs with an equal sign)

+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%281%2F2%29x-2%2C+10000%28x-1%29%29+

Now pick a test point (0,0) and evaluate it for y%3E=%281%2F2%29x-2
0%3E=%281%2F2%29%280%29-2
0%3E=-2 true. So shade the region containing (0,0). This is the region above the line
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Now pick a test point (0,0) and evaluate it for x%3E1 (remember the x=1 line should be a dashed line)
0%3E1
0%3E=-2 false. So shade the region that doesn't contain (0,0). This is the region to the right of the line.
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So the solution set will lie in the region that is created by the other two regions overlapping each other.

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