Question

).: Merp help please! Completely lost in this question:.(

Explain, in complete sentences, how you would use the graphing method to solve the following system of inequalities and what the final solution will look like on the coordinate plane.

x + y less than or equal to -5
4x - 5y > -15

Answer 1

Do you know how to graph: x + y = -5 ?
That is the first step.

Answer 2

ContourPlot[5 + x + y == 0, {x, -25/2, 5/2}, {y, -25/2, 5/2}]

Answer 3

Now, look at this: x + y less than or equal to -5

and decide whether to shade the points above the line or below.

Answer 4

(0,0) looks like a good test point.

Let's check to see if it is included in x + y ≤ -5

Is 0 + 0 ≤ -5

Is 0 ≤ -5 NO.

So, shade the region (half plane as it is called) that does not have (0,0) as part of it.

Answer 5

Something like this.

But something distinctive because we are about to draw another line on the same set of axes and do more shading. We will look for the double-shaded section as the solution set.

Answer 6

If you've done that shade, then do this.

Graph 4x - 5y = -15 on the same set of axes. Make the line dashed rather than unbroken.

Answer 7

@Futuristicmario

If what I wrote about the shading does not make sense, look at this demonstration:
https://www.youtube.com/watch?v=anQ8dGfWzAY