SOLUTION: Solve the following system of linear inequalities by graphing: x+2y>(with a line under it)3 2x-3y>(with a line under it)6

Algebra ->  Algebra  -> Graphs -> SOLUTION: Solve the following system of linear inequalities by graphing: x+2y>(with a line under it)3 2x-3y>(with a line under it)6      Log On

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Question 82581: Solve the following system of linear inequalities by graphing:
x+2y>(with a line under it)3
2x-3y>(with a line under it)6
Answer by josmiceli(9697) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+2y+%3E=+3
2x+-+3y+%3E=+6
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%283-x%29%2F2%2C%282x-6%29%2F3+%29+
The solution is the V-shaped region to the right of where both
lines touch the x-axis at (3,0)
This is found by solving each inequality for y
x+%2B+2y+%3E=+3
2y+%3E=+3+-+x
y+%3E=+%283+-+x%29%2F2 1st solution
2x+-+3y+%3E=+6
-3y+%3E=+6+-+2x
y+%3C=+%282x+-+6%29%2F3 2nd solution
Note that the inequality sign changed direction when I divided
both sides by -3
check solution
Does (3,0) satisfy both equations?
yes
Pick any point in the V-shaped region, like (6, 1)
x+%2B+2y+%3E=+3
2x+-+3y+%3E=+6
and
6+%2B+3+%3E=+3
6+-+3+%3E=+3
both are true. try some others