SOLUTION: How would solve this system of linear inequalities by graphing? x - 3y > 6 3x + 2y > 12

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Question 121807: How would solve this system of linear inequalities by graphing?
x - 3y > 6
3x + 2y > 12
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
solve this system of linear equalities, then exclude value of x where they are equal
you need to shade from the intersection the point (48/11,-6/11) (excluding this one) everything to the right

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x-3y=6

3x%2B2y=12





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


1x-3y=6 Start with the given equation



-3y=6-x Subtract +x from both sides



-3y=-x%2B6 Rearrange the equation



y=%28-x%2B6%29%2F%28-3%29 Divide both sides by -3



y=%28-1%2F-3%29x%2B%286%29%2F%28-3%29 Break up the fraction



y=%281%2F3%29x-2 Reduce



Now lets graph y=%281%2F3%29x-2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x-2%29+ Graph of y=%281%2F3%29x-2




So let's solve for y on the second equation


3x%2B2y=12 Start with the given equation



2y=12-3x Subtract 3+x from both sides



2y=-3x%2B12 Rearrange the equation



y=%28-3x%2B12%29%2F%282%29 Divide both sides by 2



y=%28-3%2F2%29x%2B%2812%29%2F%282%29 Break up the fraction



y=%28-3%2F2%29x%2B6 Reduce





Now lets add the graph of y=%28-3%2F2%29x%2B6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x-2%2C%28-3%2F2%29x%2B6%29+ Graph of y=%281%2F3%29x-2(red) and y=%28-3%2F2%29x%2B6(green)


From the graph, we can see that the two lines intersect at the point (48%2F11,-6%2F11) (note: you might have to adjust the window to see the intersection)