# Problems from Systems of inequations with two variables

Solve the following system of inequations with two variables:

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

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### 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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