SOLUTION: 3y>9-2x 2x+3y<-6

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Question 1205412: 3y>9-2x
2x+3y<-6
Found 3 solutions by josgarithmetic, greenestamps, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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3y>9-2x
2x+3y<-6
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Put both into slope-intercept form and graph each region separately. The overlapping parts is your graph, which will exclude the reference lines.

system%28y%3E-2x%2F3%2B3%2C3y%3C-2x-6%29

system%28y%3E-2x%2F3%2B3%2Cy%3C-2x%2F3-2%29

The graphed reference lines:
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-2x%2F3%2B3%2C-2x%2F3-2%29

But in this example, no overlap. Two separated regions.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Move the "x" term in the first inequality; the two inequalities are then

2x+3y > 9
2x+3y < -6

Since the value of an expression can never be both greater than 9 and less than -6, there is no solution.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

3y>9-2x is the same as 2x+3y > 9 when adding 2x to both sides.

We have this system of inequalities
system%282x%2B3y+%3E+9%2C2x%2B3y+%3C+-6%29
which is equivalent to this system
system%28z+%3E+9%2C+z+%3C+-6%29
where z = 2x+3y

What number is larger than 9 AND smaller than -6 at the same time?
No such number exists.
There are no solutions.

In reference to tutor josgarithmetic's graph, 3y>9-2x aka 2x+3y > 9 has you shade above the line 2x+3y = 9 (the red line in their graph).
while 2x+3y < -6 means you shade below the parallel green line 2x+3y = -6
These shaded regions do not overlap, which is a visual indicator of "no solutions"