SOLUTION: Graph the system of inequalities -2x+3y>or = to -12 X+y<3

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Question 935586: Graph the system of inequalities
-2x+3y>or = to -12
X+y<3

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
-2x%2B3y%3E=+-12.............(1)
x%2By%3C3...............(2)
__________________________________solve both for y
y%3E=+%282%2F3%29x-4.............(1)
y%3C-x%2B3...............(2)
graph the first inequality:
y%3E=+%282%2F3%29x-4.............(1)
you need two points to draw a graph:
if x=0 then y%3E=-4; so, first point is (0,-4)
if y=0 then 0%3E=%282%2F3%29x-4=>4%3E=%282%2F3%29x=>4%2F%282%2F3%29%3E=x=>6%3E=x; so, second point is (6,0)

since we have >=, line is part of solution
so, shade a part above a line; that is solution





graph second inequality on the same graph

y%3C-x%2B3...............(2)
if x=0 then y%3C3; so,we take y=3 first point is (0,3)
if y=0 then x%3C3; so, second point is (3,0)



since given that y is less then-our line is not part of solution and need to be dashed line (I can't do it here)
now shade solution part


finally, we can shade solution to the system: