# Problems from Systems of inequations with two variables

Solve the following system of inequations with two variables:

$$\left\{ \begin{array}{l} x-2y < 2 \\ y+x > 1-x \end{array}\right.$$$See development and solution ### 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 $$y = 1-2x$$

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