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

Jun 15, 2015

Graph the system of 3 linear functions in 2 variables:
(1) $x + y < 8$
(2) $x \ge 0$
(3) $y \ge 0$

Explanation:

First graph the Line y1 = -x + 8.
The solution set of the inequality (1) is the area below this line. Color it.
$x \ge 0 \mathmr{and} y \ge 0$ . 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.