SOLUTION: solve 5x + 3y > -6 and 2y + x < 6 (inequalities)

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Question 698466: solve 5x + 3y > -6 and 2y + x < 6 (inequalities)
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve
5x + 3y > -6
Solve for "y":
y > (-5/3)x - 2
---
Graph the boundry line as a dashed line:
y = (-5/3)x - 2
Shade the half-plane ABOVE the boundary because you want
y to be greater than (-5/3)x-2:::
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-5%2F3%29x-2%29
---------------------------------------------------
and 2y + x < 6
y < (-1/2)x + 3
----
Boundary y = (-1/2)x + 3
Shade the half-plance BELOW te boundary:
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B3%29
-------
The intersection of the two half-planes is the solution
set for the system on inequalities.
===================
Cheers,
Stan H.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
5x+%2B+3y+%3E+-6 ...the graph is a line and you graph it as equality
5x+%2B+3y=-6 find two points that lie on a line
easiest way is to find x and y-intercept
set x=0 and find y-intercept
5%2A0+%2B+3y=-6
+3y=-6
+y=-2
set y=0 and find x-intercept
5x+%2B+3%2A0=-6
+5x=-6
+x=-6%2F5
now plot these points and draw a dashed line through because you have inequality 5x+%2B+3y+%3E+-6 and shade all area above the line
Solved by pluggable solver: Plot Any Inequality
Graphing function 5x%2B3y%3E-6:

graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+5x%2B3y%3E-6+%29


do same with 2y+%2B+x+%3C+6+

set x=0 and find y-intercept
2y+%2B+0+=6
+2y=6
+y=3
set y=0 and find x-intercept
2%2A0+%2B+x+=6
+x=6
Solved by pluggable solver: Plot Any Inequality
Graphing function 2y%2Bx%3C6:

graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2y%2Bx%3C6+%29



and as a system, solution will be shaded area that overlaps

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2y+%2B+x+%3C+6%2C+5x%2B3y%3E-6%29+