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# Determining the Type of Linear System

## Identify consistent, inconsistent, and dependent systems

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Determining the Type of Linear System

### Determining the Type of Linear System

• A consistent system will always give exactly ___ solution.
• An inconsistent system will yield a statement that is _______ (like \begin{align*}0 = 13\end{align*} ).
• A dependent system will yield a statement that is _______ (like \begin{align*}9 = 9\end{align*} ).

To determine the type of linear system...

1. Solve the systems of equations using substitution, linear combination, or any other method.  Remember, the solution to the system of equations are quantities for x, y, (and z) that satisfy all equations.
2. If you can successfully solve the system of equations with only one solution, you know it is consistent.
3. If the "solution" to the system of equations turns out to be false, you know it is inconsistent.
4. If the solution to the system of equations turns out to be always true regardless of the situation, you know it is dependent.

### Practice

1. \begin{align*}5x - 4y = 1\!\\ -10x + 8y = -30\end{align*}
2. \begin{align*}4x + 5y = 0\!\\ 3x = 6y + 4.5\end{align*}
3. \begin{align*}-2y + 4x = 8\!\\ y - 2x = -4\end{align*}
4. \begin{align*}x - \frac{1}{2}y = \frac{3}{2}\!\\ 3x + y = 6\end{align*}

For more practice, look here.

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