Question

Graph the solution to the following system of inequalities. Choose one point in the solution of the system and prove it
mathematically.
2x - 3y<=6
y< -1/2x
Include the graph of the system of inequalities and the proof of the solution.

Answer 1

Answer:

Step-by-step explanation:

$2x - 3y\leq 6$ ==> $y\leq \frac{2}{3}x-2$

$y < -\frac{1}{2} x$

$2x - 3y\leq 6$

$-2x$      $-2x$

$-3y\leq -2x+6$

$\frac{-3y}{-3} \leq \frac{-2x+6}{-3}$

$y\geq \frac{2}{3}x-2$

$y\geq \frac{2}{3}x-2$  

$y < -\frac{1}{2} x$

Check you answer using (-1,-1)

$y\geq \frac{2}{3}x-2$

$-1\geq \frac{2}{3}(-1)-2$

$-1\geq -\frac{2}{3}-2$

$-1\geq -\frac{2}{3}-\frac{6}{3}$

$-1\geq -\frac{8}{3}$

$-3(-1\geq -\frac{8}{3})$

$3\geq 8$

True statement

Hope this helps!