# How do you solve this system of inequalities: #y < \frac { 1} { 3} x + 4 and y \geq - x + 1#?

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**Given:**

We are given the **System of Inequalities**:

**and**

**graph created using GeoGebra**

**graph created using GeoGebra**

**and** **combined graphs created using GeoGebra**

If you observe closely, you will find the **solution** in a visual form.

The **solution to the system of inequalities** is **the darker shaded region, which is the overlap of the two individual regions**.

If you want to view just the solutions, please refer to the image below:

**Note:**

If the inequality is < or >, graph of the equation has a **dotted line**.

If the inequality is ≤ or ≥, graph of the equation has a **solid line. **

This line **divides the xy- plane into two regions:** a region that **satisfies the inequality**, and **a region that does not.**

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