Question

I need help with graphing the system of linear inequalities. Question is posted in the comment section of this question!

Answer 1

\[2x - 3y \le 0 \]
\[3x+2y \le 6\]

Answer 2

Put both equations in y-intercept form to graph!
\[2x - 3y \le 0\]
\[-3y \le -2x\]
\[y \ge \frac{ 2x }{ 3 }\] Have to switch the sign cause you divided by a negative.

\[3x + 2y \le 6\]
\[2y \le -3x + 6\]
\[y \le \frac{ -3x }{ 2 } + 3\]

Now both are set!
(1) \[y \ge \frac{ 2x }{ 3 }\]
(2) \[y \le \frac{ -3x }{ 2 } + 3\]

Simply plot these graphs by ignoring the greater than or less than. Pretend they are simply equal to draw them. Because both are something or "equal to", use solid lines for both lines. Then, simply shade the region indicated. If less than, shade below the line you draw. If greater than, shade above the line you draw. The region shaded by both lines is the solution ^_^

Hope this helps!