### 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...

- 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.* - If you can successfully solve the system of equations with only one solution,
**you know it is consistent.** - If the "solution" to the system of equations turns out to be false,
**you know it is inconsistent.** - If the solution to the system of equations turns out to be always true regardless of the situation,
**you know it is dependent.**

### Practice

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

For more practice, look here.