{ x ≤-1 y ≥ 3 .

Name: Problem 304, Chapter 5: Elementary Algebra
Uploaded: 2021-08-02T22:12:36-08:00
Duration: 2 min 2 s
Channel: Luke Waitrovich
Description: { x ≤-1 y ≥ 3 .

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Key Concepts

Systems of Inequalities

A system of inequalities consists of multiple inequality constraints that must be satisfied simultaneously. The solution to the system is the intersection of the solution sets of the individual inequalities, often referred to as the feasible region.

Graphical Representation

Graphing is a visual method for representing inequalities on the coordinate plane by drawing boundary lines and shading regions that satisfy the given conditions. This visual approach helps in identifying the common solution area of a system of inequalities, useful in various applications such as optimization problems.

Inequalities

Inequalities are mathematical expressions that show the relative size or order of two values, using symbols such as <, >, ?, and ?. They establish a range of potential solutions rather than a single value, which is essential in understanding relationships between quantities.

Linear Inequalities

Linear inequalities involve expressions of the first degree and typically represent half-planes when graphed on a coordinate system. Understanding how to manipulate and solve these is key to identifying the solution sets that satisfy each inequality.

Transcript

00:01 Hello and welcome to this video where i'm going to graph a system of linear inequalities.

00:05 So our goal is to find a portion of this graph that will work for both of the inequalities.

00:10 And we're going to do that is by graphing each of these separately.

00:13 So let's start off with x is less than or equal to negative 1.

00:16 In order to get the graph, i'm going to pretend that this is essentially x equals 1.

00:20 So that's the first thing i'm going to do.

00:22 Now anything you have an x equals, that's a vertical line.

00:25 So i'm going to go to a vertical line over at 1 on the x -axis, and now i'm going to draw it.

00:30 And since it is less than or equal to, it's going to be a solid line.

00:34 So i'll draw a solid line right there.

00:37 Now i'm going to do something kind of similar for the other one.

00:40 I'm going to treat this as y equals 3, and y equals is a horizontal line compared to a vertical line.

00:47 So you go to 3 on the y -axis.

00:50 Draw that.

00:51 Perfect.

00:52 Now i need to think about the shading.

00:54 So for the red line, since it's greater than or equal to, i'm going to shade above it.

00:59 So i'm going to put arrows pointing...

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