SOLUTION: Solve by graphing. 3x + 4y ≤ 12 x + 3y ≤ 6 x ≥ 0 y ≥ 0 Please show work so I can understand.

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Question 173525: Solve by graphing.
3x + 4y ≤ 12
x + 3y ≤ 6
x ≥ 0
y ≥ 0
Please show work so I can understand.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
I'll give you the method, and then you can do the work.

Start with your original inequality and then replace the inequality sign with an equals sign. You will have the equation of a straight line. Graph the straight line. When you draw your line, look at your inequality symbol in the original inequality. If it includes equals, either ≤ or ≥, then graph your line as a solid line. Otherwise, graph your line as a dashed line. Since all 4 of your given problems include equals, use solid lines for all 4.

Next, select a point that is NOT on the line. (0,0) is an excellent choice IF the line does not pass through the origin. (1,0), (0,1), and (1,1) are also good choices if (0,0) is contained in the line. Take the coordinates for the point you selected and substitute the x and y values from the ordered pair back into the original inequality.

If the result is a true statement, shade in the half-plane on the SAME side of the line that the selected point is on.

If the result is a false statement, shade in the half-plane on the OTHER side of the line from the selected point.

Hint for the last two: is the equation of the y-axis, is the equation of the x-axis.

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