SOLUTION: Please help me to determine graphically the solution set for the following set of inequalities:
x +2y > or = to 3
5x - 4y < or = to 20
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Question 428805: Please help me to determine graphically the solution set for the following set of inequalities:
x +2y > or = to 3
5x - 4y < or = to 20
y < or = to 2
x > or = to 0
y > or = to 0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Step 1: Change the relationship symbol to "=". Graph the resulting line. If the original relationship symbol was 
or 
, do it with a dashed or broken line. If your symbol was 
or 
, graph the equation with a solid line.
Step 2: Pick any point on the coordinate plane that does not lie on the line you just graphed. If the line does not pass through the origin, )
then the origin is an excellent choice for this step. If the line does pass through the origin, select a point other than the origin -- I recommend a point that has small integer coordinates.
Step 3: Substitute the values of the coordinates of the point chosen in Step 2 for the corresponding variables in the inequality you started with in Step 1.
Step 4: Do the appropriate arithmetic to determine whether the substitution created a true statement or not. If you created a true statement, shade in the side of the line containing the point selected in Step 2. If you created a false statement, shade in the side of the line that does not contain the selected point.
Step 5: Repeat steps 1 through 4 for each of other inequalities. If this is a system of inequalities and you want the solution set of the system, graph them all on the same coordinate plane. The solution set will be the region where the shaded areas overlap. If the shaded areas do not overlap at all, the solution set is the empty set. Note that points on any dashed boundary lines, in the case where you do not have a or relationship, are not included in the solution set. Points on solid boundary lines are included in the solution set.
John
My calculator said it, I believe it, that settles it
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