Solve the following system of inequations with two variables:

$$$ \left\{ \begin{array}{l} x-2y < 2 \\ y+x > 1-x \end{array}\right. $$$

### Development:

We will start by isolating the $$y$$ on one side of the inequation and the $$x$$ on the other:

$$$ \left\{ \begin{array}{l} x-2y < 2 \\ y+x > 1-x \end{array}\right. \Rightarrow \left\{ \begin{array}{l} \dfrac{x-2}{2} < y \\ y > 1-2x \end{array}\right. \Rightarrow \left\{ \begin{array}{l} y > \dfrac{x-2}{2} \\ y > 1-2x \end{array}\right. $$$

the solution region of the system will cover the areas over the straight line $$ y = \dfrac{x-2}{2} $$ and below the straight line $$ y = 1-2x $$.

### Solution:

The solution region of the system will cover the areas over the straight line $$ y = \dfrac{x-2}{2} $$ and below the straight line $$ y = 1-2x $$