# Solve each of the following system of equations in R.

Question:

Solve each of the following system of equations in R.

17. $\frac{2 x+1}{7 x-1}>5, \frac{x+7}{x-8}>2$

Solution:

$\frac{2 x+1}{7 x-1}>5$

$\Rightarrow \frac{2 x+1}{7 x-1}-5>0$

$\Rightarrow \frac{2 x+1-35 x+5}{7 x-1}>0$

$\Rightarrow \frac{6-33 x}{7 x-1}>0$

$\Rightarrow x \in\left(\frac{1}{7}, \frac{2}{11}\right)$      ...(i)

Also, $\frac{x+7}{x-8}>2$

$\Rightarrow \frac{x+7}{x-8}-2>0$

$\Rightarrow \frac{x+7-2 x+16}{x-8}>0$

$\Rightarrow \frac{23-x}{x-8}>0$

$\Rightarrow x \in(-\infty, 8) \cup(23, \infty) \quad \ldots \ldots($ ii $)$

Hence, the solution to the given set of inequalities is the intersection of (i) and (ii), which is empty.

$\therefore x \in \emptyset$