SOLUTION: Write a system of inequalities whose solution is represented by the shaded region shown on the graph at the right http://prntscr.com/bat1nx?

Question 1036626: Write a system of inequalities whose solution is represented by the shaded region shown on the graph at the right http://prntscr.com/bat1nx?
Found 2 solutions by JBarnum, solver91311:
Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First thing to do is write the equations of the boundary lines.

Note that the solid boundary line goes right one and up one, so the slope is +1. And it intercepts the y-axis at (0,-3). That gives us an equation, in slope-intercept form, of:

I'll leave derivation of the other equation to you.

Next is to determine which of the four inequality symbols is appropriate. Since this is a solid line, the desired inequality is inclusive of equals, so you must use either or -- but which one?

Since the point (0,0) is located in the shaded half-plane with the equation we derived as a boundary, then substituting 0 for and 0 for should create a true statement if you have used the inequality symbol of the correct sense. So which is correct?

or

Find the correct symbol for the other inequality using the same process. Remember, a dashed line excludes equality, so you need to decide between < and >.

John

My calculator said it, I believe it, that settles it

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