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!
Things To Remember:
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!
Tell whether the linear system has no solution or infinitely many solutions.
Solve this using graphing AND elimination!
Equation 1 ----------> 3x+2y=10
Equation 2 ----------> 3x+2y=2
Solve this using Graphing and Substitution!
Equation 1 --------> x-2y=-4
Equation 2 ---------> y=1/2x+2