Question 151864
Solve following inequalities, create table to show answers.

2x + 2y > or equal to 6 
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x + y >= 3
y >= -x + 3
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Graph the EQUALITY:
If x = 0, y = 3
If x = 1, y = 2
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Plot the two points (0,3) and (1,2) and draw a solid line thru them:
{{{graph(400,300,-10,10,-10,10,-x+3)}}}
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Since you also want y GREATER THAN -x + 3, shade the half-plane
ABOVE the line.
The union of the line and the half-plane is the entire solution 
set for your problem.
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Cheers,
Stan H.