Solve each of the following system of equations in R. 2. 2x − 7 > 5 − x,

We have, $2 x-7>5-x$

$\Rightarrow 2 x+x>5+7$

$\Rightarrow 3 x>12$

$\Rightarrow x>4$

$\Rightarrow x \in(4, \infty) \ldots$ (i)

Also, $11-5 x \leq 1$

$\Rightarrow 5 x \geqslant 11-1$

$\Rightarrow x \geqslant 2$

$\Rightarrow x \in[2, \infty) \ldots$ (ii)

$S$ olution set of the given set of inequations is intersection of (i) and (ii)

$(4, \infty) \cap[2, \infty)=(4, \infty)$

Thus, the solution set of the given set of inequations is $(4, \infty)$.