Question

How do you graph the system `x+y<8` and `x>=0` and `y>=0`?

Answer 1

Graph the system of 3 linear functions in 2 variables:
(1) `x + y < 8`
(2) `x>= 0`
(3) `y >= 0`

Explanation:

First graph the Line y1 = -x + 8.
The solution set of the inequality (1) is the area below this line. Color it.
`x >= 0 and y >= 0` . The solution set is the total area of Quadrant I.
The combined solution set is the commonly shared area.

Note. The half-axis Ox and Oy are both included in the solution set.