Solve each of the following system of equations in R. 11. 4x − 1 ≤ 0, 3 − 4x < 0

We have, $4 x-1 \leq 0$

$\Rightarrow 4 x \leq 1$

$\Rightarrow x \leq \frac{1}{4} \quad$ (Dividing both the sides by 4 )

$\Rightarrow x \in\left(-\infty, \frac{1}{4}\right] \quad \ldots(\mathrm{i})$

Also, $3-4 x<0$

$\Rightarrow 0>3-4 x$

$\Rightarrow 4 x>3$

$\Rightarrow x>\frac{3}{4} \quad$ Dividing both sides by 4

$\Rightarrow x \in\left(\frac{3}{4}, \infty\right) \quad \ldots$ (ii)

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

But, $\left(-\infty \frac{1}{4}\right) \cap\left(\frac{3}{4}, \infty\right)=\phi$

Thus, the given set of inequations has no solution.