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

Feb 4, 2018

color(blue)((1/3)x+4 > y >= -x+1

#### Explanation:

Given:

We are given the System of Inequalities:

color(brown)(y < (1/3)x+4  and

color(brown)(y >= (-x)+1

color(green)(Step.1

color(brown)(y < (1/3)x+4  - Image of the graph created using GeoGebra

color(green)(Step.2

color(brown)(y >= (-x)+1 - Image of the graph created using GeoGebra

color(green)(Step.3

color(brown)(y < (1/3)x+4  and color(brown)(y >= (-x)+1 - Image of the 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.

color(green)(Step.4

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.