# What are the boundaries of x and y if 2x - 3y >= 9 and - x - 4y >= 8??

Jan 20, 2018

$x \ge \frac{37}{25}$
$y \ge \frac{25}{11}$.

#### Explanation:

$2 x - 3 y \ge 9$

$\left(- x - 4 y \ge 8\right) \cdot 2 = - 2 x - 8 y \ge 16$

add $2 x - 3 y \ge 9$
+ $- 2 x - 8 y \ge 16$

You get $11 y \ge 25$
So, $y \ge \frac{25}{11}$.
You plug in $\frac{25}{11}$ into one of the equation and solve for x.
$2 x - 3 \left(\frac{25}{11}\right) \ge 9$
$2 x \ge \frac{74}{25}$
$x \ge \frac{37}{25}$