Question

Match the vocabulary word to its correct definition. 1. consistent equations A system of linear equations that do not contain any common points. 2. dependent equations A set of linear equations that coincide and share every point as a point of intersection. Also known as a dependent and consistent solution. 3. inconsistent equations 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. 4. infinitely many solutions A system of linear equations that contain at least one common point. 5. independent equations A system of linear equations that rely on each other for the algebraic or graphic form of the equation. 6. no solution A system of linear equations that do not rely on each other for the algebraic or graphic form of the equation. 7. one solution A set of parallel lines that will never share a point of intersection. Considered to be an inconsistent solution.

Answer 1

The three types of solution sets:   A system of linear equations can have no solution, a unique solution or infinitely many solutions.

Match The Vocabulary words:  

1. Consistent Equations ==>  A system of linear equations that contain at least one common point.

2. Dependent Equations ===>   A system of linear equations that rely on each other for the algebraic or graphic form o f the equation

3. Inconsistent Equations ===>  A system of linear equations that do not contain any common points

4. Infinitely Many Solutions ===>  A system has infinitely many solutions when it is consistent and the number of variables is more than the number of nonzero rows in the rref of the matrix.

5. Independent Equations  ===>   A system of linear equations that do not rely on each other for the algebraic or graphic form of the equation.

6. No Solution ===>   A set of parallel lines that will never share a point of intersection. Considered to be an inconsistent solution ("empty set").

7. One Solution  ===>  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!!!                                    : )

Answer 2

Here are the words and their corresponding definitions