Show All Notes Hide All Notes

Section 7.4 : More on the Augmented Matrix

For each of the following systems of equations convert the system into an augmented matrix and use the augmented matrix techniques to determine the solution to the system or to determine if the system is inconsistent or dependent.

1. \(\begin{align*}8x + y & = 13\\ 3x + 4y & = - 6\end{align*}\)
2. \(\begin{align*}x - 3y & = 7\\ - 2x + 6y & = 4\end{align*}\)
3. \(\begin{align*} - 12x + 6y & = - 12\\ 4x + 2y & = - 2\end{align*}\)
4. \(\begin{align*}3x + 6y & = 12\\ - 4x - 7y & = - 12\end{align*}\)
5. \(\begin{align*}12x - 6y & = 18\\ 4x - 2y & = 6\end{align*}\)
6. \(\begin{align*} - 5x + 10y & = 1\\ x - 2y & = - 8\end{align*}\)
7. \(\begin{align*}7x + 6y & = 0\\ 2x + 3y & = 0\end{align*}\)
8. \(\begin{align*} - 8x + 24y & = 12\\ 10x - 30y & = - 15\end{align*}\)
9. \(\begin{align*} - 2x + 3y & = 24\\ 3x - 8y & = - 57\end{align*}\)
10. \(\begin{align*}6x + 4y & = - 20\\ 7x + 3y & = - 35\end{align*}\)
11. \(\begin{align*} - 3x + 7y + 2z & = - 8\\ - 2x + 5y - z & = - 10\\ 8x - 2y + 3z & = 38\end{align*}\)
12. \(\begin{align*}6x + 4y - 8z & = - 56\\ - x - 4y + z & = 5\\ 3x + y + 9z & = 10\end{align*}\)
13. \(\begin{align*}2x + 6y - z & = 1\\ - x + 2y + 9z & = - 19\\ 4x + 3y - 7z & = 25\end{align*}\)