Can someone please help me out with this algebra problem, an explaination would be appreciated.?

Question

Solve each system of inequalities by graphing

x+y<8
x greater then or less then 0
y greater then or less then 0

( fyi, greater then or less than is this > with a line underneath)

technically I already have the answer

at y i have it plotted at 6 (y vertical line)

and at x i have it plotted at 7

My problem is I keep looking at this problem having no clue how that answer is true. I also dont understand the whole shade up or shade down thing (in this problem its shaded below so that with the line drawn it looks like a right triangle)

so to sum it up could someone tell me how to graph these types of problems?

Answer 1

x is 8 and y is 8
you plug in 0 for one and answer, so on a graph plot 8 on the Y-axis and 8 on the X-axis, it makes sense (solid line, and shaded underneath).

Answer 2

≥ means greater than or equal to
≤ means less than or equal to

The best way to solve these is to solve the inequality so that you only have y on the left. Then you pretend the inequality sign is an equals sign. Graph this equation. If the inequality includes the 'equal to' part then it should be a solid line. Otherwise use a dotted line because these points aren't actually included. It just gives you the border of what you need to shade. Then shade the appropriate region depending on whether your result is > or < than something else. If you have y > something the shaded region should be above the graph of the equation.