Problems from Systems of inequations with two variables

Development:

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

$$\{\begin{array}{l}x-2y<2\\ y+x>1-x\end{array}\Rightarrow \{\begin{array}{l}{\displaystyle \frac{x-2}{2}}<y\\ y>1-2x\end{array}\Rightarrow \{\begin{array}{l}y>{\displaystyle \frac{x-2}{2}}\\ y>1-2x\end{array}$$

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

Solution:

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

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