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Section 7.1 : Linear Systems with Two Variables

For problems 1 – 5 use the Method of Substitution to find the solution to the given 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. \(\begin{align*}12x - 6y & = 18\\ 4x - 2y & = 6\end{align*}\)

For problems 6 – 10 use the Method of Elimination to find the solution to the given system or to determine if the system is inconsistent or dependent.

1. \(\begin{align*} - 5x + 10y & = 1\\ x - 2y & = - 8\end{align*}\)
2. \(\begin{align*}7x + 6y & = 0\\ 2x + 3y & = 0\end{align*}\)
3. \(\begin{align*} - 8x + 24y & = 12\\ 10x - 30y & = - 15\end{align*}\)
4. \(\begin{align*} - 2x + 3y & = 24\\ 3x - 8y & = - 57\end{align*}\)
5. \(\begin{align*}6x + 4y & = - 20\\ 7x + 3y & = - 35\end{align*}\)