Systems of inequations with two variables
Solve the following system of inequations with two variables:
$$\left\{ \begin{array}{l} x-2y < 2 \\ y+x > 1-x \end{array}\right. $$
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 $.
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 $