Question 1036626
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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 <i>equation</i>, in slope-intercept form, of:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x\ -\ 3]


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 *[tex \Large \leq] or *[tex \Large \geq] -- 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 *[tex \Large y] and 0 for *[tex \Large x] should create a true statement if you have used the inequality symbol of the correct sense.  So which is correct?


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ \leq\ 0\ -\ 3]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ \geq\ 0\ -\ 3]


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
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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