<u>The three types of solution sets:
A system of linear equations can have no solution, a unique solution or infinitely many solutions.
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<u>Match The Vocabulary words: </u>
1. <u>Consistent Equations</u> ==> A system of linear equations that contain at least one common point.
2. <u>Dependent Equations</u> ===> A system of linear equations that rely on each other for the algebraic or graphic form o f the equation
3. <u>Inconsistent Equations</u> ===> A system of linear equations that do not contain any common points
4. <u>Infinitely Many Solutions</u> ===> A system has <u>infinitely many solutions</u> when it is consistent and the number of variables is more than the number of nonzero rows in the rref of the matrix.
5. <u>Independent Equations</u> ===> A system of linear equations that do not rely on each other for the algebraic or graphic form of the equation.
6. <u>No Solution </u>===> A set of parallel lines that will never share a point of intersection. Considered to be an inconsistent solution ("empty set").
7. <u>One Solution </u> ===> A set of linear equations that share a common point known as the point of intersection (x,y). The solution, (x,y) is an independent and consistent solution.
Hope that helps!!! : )