 Table of Contents Solving Linear Systems of Equations - Dependent Systems The goal in solving a linear system of equations is to find the values of the.

Presentation on theme: "Table of Contents Solving Linear Systems of Equations - Dependent Systems The goal in solving a linear system of equations is to find the values of the."— Presentation transcript:

Table of Contents Solving Linear Systems of Equations - Dependent Systems The goal in solving a linear system of equations is to find the values of the variables that satisfy all of the equations in the system. Sometimes an infinite number of solutions is found. Example: Solve the following system of equations...

Table of Contents Slide 2 Solving Linear Systems of Equations - Dependent Systems Using the addition method we find... Since both variables were eliminated, and the result is clearly true, what does this say about the solutions to the system? Solve each of the equations for y...

Table of Contents Slide 3 Solving Linear Systems of Equations - Dependent Systems It turns out that the original equations are equivalent. This means that any solution to the first equation will be a solution to the second equation. The solution set is written in the following way: Let x = t, t any real number. Since y = 4 - x, let y = 4 - t. Solution: ( x, 4 - t), t any real number. For example, if t = 3, then (3, 1) is a solution. If t = -2, then (-2, 6) is a solution.

Table of Contents Slide 4 Solving Linear Systems of Equations - Dependent Systems Since t can be any real number, there are infinitely many solutions to the system. Such a system is called a Dependent System. Systems of three equations in three unknowns can also be dependent with similar algebraic results