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Solving Linear Systems: Special Cases

Solving Linear Systems: Special Cases

Author: Sara Gorsuch

Looking at situations where linear systems have no solution, and looking at situations where linear systems have infinite solutions.

In this packet I will explain a linear system, and no solution and Infinite Solutions. I will give example problems and show what exactly they mean and how to go through the steps of the two!

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Linear Systems, Parallel and Same Line.

  Things To Remember:

Solution of a system of Linear equations: A ordered pair (x,y) that satisfies each equation in the system.

Linear System/System of Linear Equations: Two or more linear equations in the same variables. 

ALWAYS check you answers algebraically. 

A "system" of equations is a set/collections of equations that are all dealt will all together at once!

The simplest for of Linear Systems have two equations and two variables. 

When dealing with odd Linear Systems such as one with no solution and one with infinite solutions, just remember this!

If it has infinite solutions, it is two equations that are the same line. If there are two equations that are the same line on a graph the linear system has infinite solutions!

If it has NO solutions, it is two equations that lines are parallel to each other. If you see two equations that have parallel lines on a graph, then there is no solutions. This is because those two lines will never intersect and therefore have no solutions!

Three Different Types Of Solutions




Try These Problems on Your Own!

 Tell whether the linear system has no solution or infinitely many solutions.

Solve this using graphing AND elimination!


Example One

Equation 1 ---------->    3x+2y=10

Equation 2 ---------->  3x+2y=2


Solve this using Graphing and Substitution!

Example Two 

Equation 1 --------> x-2y=-4


Equation 2 ---------> y=1/2x+2