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## Math 9.61

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\begin{figure}[ht!]
\vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg}
\end{figure}

\vspace{-15mm}\begingroup
\centering
\LARGE Simultaneous Equations \\[0.5em]
\endgroup

\fontsize{12pt}{16pt}\selectfont
\subsection{Exercise 1. Solve for $x$ and $y$..}
\begin{multicols}{2}
\begin{enumerate}[label=\arabic*)]
\setlength\itemsep{2em}
\item $$\begin{array}{rl}-3x + 4y &= 8 \\ -1x + 2y &= 2\end{array}$$ \\@$x = -4, y = -1$
\item $$\begin{array}{rl}-7x + 5y &= 5 \\ 6x - 4y &= -5\end{array}$$ \\@$x = \frac{-5}{2}, y = \frac{-5}{2}$
\item $$\begin{array}{rl}-2x + 1y &= -3 \\ 3x + 1y &= 5\end{array}$$ \\@$x = \frac{8}{5}, y = \frac{1}{5}$
\item $$\begin{array}{rl}3x + 4y &= 6 \\ 3x + 5y &= 8\end{array}$$ \\@$x = \frac{-2}{3}, y = 2$
\item $$\begin{array}{rl}4x + 5y &= -3 \\ 1x - 1y &= -1\end{array}$$ \\@$x = \frac{-8}{9}, y = \frac{1}{9}$
\item $$\begin{array}{rl}-8x - 3y &= 2 \\ 6x + 2y &= -2\end{array}$$ \\@$x = -1, y = 2$
\item $$\begin{array}{rl}3x + 5y &= 5 \\ 2x + 6y &= 4\end{array}$$ \\@$x = \frac{5}{4}, y = \frac{1}{4}$
\item $$\begin{array}{rl}-1x - 4y &= 1 \\ 1x + 7y &= -7\end{array}$$ \\@$x = 7, y = -2$
\item $$\begin{array}{rl}2x - 4y &= 8 \\ 1x - 1y &= 5\end{array}$$ \\@$x = 6, y = 1$
\item $$\begin{array}{rl}-1x - 6y &= 3 \\ 2x + 8y &= -2\end{array}$$ \\@$x = 3, y = -1$
\item $$\begin{array}{rl}-1x + 3y &= 6 \\ 1x - 2y &= -2\end{array}$$ \\@$x = 6, y = 4$
\item $$\begin{array}{rl}1x + 8y &= -7 \\ 1x + 6y &= -5\end{array}$$ \\@$x = 1, y = -1$
\item $$\begin{array}{rl}5x + 6y &= 7 \\ -1x - 3y &= -3\end{array}$$ \\@$x = \frac{1}{3}, y = \frac{8}{9}$
\item $$\begin{array}{rl}-4x - 4y &= 5 \\ -5x - 7y &= 7\end{array}$$ \\@$x = \frac{-7}{8}, y = \frac{-3}{8}$
\item $$\begin{array}{rl}-3x - 5y &= -1 \\ -2x - 5y &= 1\end{array}$$ \\@$x = 2, y = -1$
\item $$\begin{array}{rl}5x - 8y &= 7 \\ 2x - 4y &= 4\end{array}$$ \\@$x = -1, y = \frac{-3}{2}$
\item $$\begin{array}{rl}-7x + 7y &= -3 \\ -4x + 5y &= -3\end{array}$$ \\@$x = \frac{-6}{7}, y = \frac{-9}{7}$
\item $$\begin{array}{rl}1x - 2y &= -5 \\ -2x + 1y &= 4\end{array}$$ \\@$x = -1, y = 2$
\item $$\begin{array}{rl}4x - 3y &= 5 \\ 3x - 4y &= 6\end{array}$$ \\@$x = \frac{2}{7}, y = \frac{-9}{7}$
\item $$\begin{array}{rl}-1x + 1y &= 1 \\ -7x + 6y &= -2\end{array}$$ \\@$x = 8, y = 9$
\end{enumerate}
\end{multicols}

\newpage

\begin{figure}[ht!]
\vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg}
\end{figure}

\vspace{-15mm}\begingroup
\centering
\LARGE Simultaneous Equations \\[0.5em]
\endgroup

\fontsize{12pt}{16pt}\selectfont
\subsection{Exercise 2. Solve for $x$ and $y$..}
\begin{multicols}{2}
\begin{enumerate}[label=\arabic*)]
\setlength\itemsep{2em}
\item $$\begin{array}{rl}3x + 1y &= -8 \\ 1x + 1y &= -4\end{array}$$ \\@$x = -2, y = -2$
\item $$\begin{array}{rl}-1x - 1y &= -6 \\ 1x + 2y &= 4\end{array}$$ \\@$x = 8, y = -2$
\item $$\begin{array}{rl}-2x - 7y &= 8 \\ -1x - 1y &= 1\end{array}$$ \\@$x = \frac{1}{5}, y = \frac{-6}{5}$
\item $$\begin{array}{rl}-2x - 2y &= 1 \\ 5x + 8y &= -5\end{array}$$ \\@$x = \frac{1}{3}, y = \frac{-5}{6}$
\item $$\begin{array}{rl}2x - 2y &= 2 \\ -3x + 1y &= -6\end{array}$$ \\@$x = \frac{5}{2}, y = \frac{3}{2}$
\item $$\begin{array}{rl}7x + 5y &= 3 \\ -5x - 4y &= -2\end{array}$$ \\@$x = \frac{2}{3}, y = \frac{-1}{3}$
\item $$\begin{array}{rl}1x - 3y &= 2 \\ -3x + 3y &= -7\end{array}$$ \\@$x = \frac{5}{2}, y = \frac{1}{6}$
\item $$\begin{array}{rl}-3x + 4y &= -4 \\ -4x + 5y &= -7\end{array}$$ \\@$x = 8, y = 5$
\item $$\begin{array}{rl}-2x - 8y &= 5 \\ 3x + 8y &= -6\end{array}$$ \\@$x = -1, y = \frac{-3}{8}$
\item $$\begin{array}{rl}-1x + 2y &= -4 \\ -3x + 4y &= -6\end{array}$$ \\@$x = -2, y = -3$
\item $$\begin{array}{rl}-1x + 2y &= -1 \\ -6x + 3y &= -4\end{array}$$ \\@$x = \frac{5}{9}, y = \frac{-2}{9}$
\item $$\begin{array}{rl}-5x + 6y &= -1 \\ 3x - 5y &= 2\end{array}$$ \\@$x = -1, y = -1$
\item $$\begin{array}{rl}-2x - 3y &= -1 \\ 5x + 4y &= 6\end{array}$$ \\@$x = 2, y = -1$
\item $$\begin{array}{rl}-3x + 2y &= 3 \\ 5x - 3y &= -8\end{array}$$ \\@$x = -7, y = -9$
\item $$\begin{array}{rl}3x - 3y &= 4 \\ 2x + 1y &= 1\end{array}$$ \\@$x = \frac{7}{9}, y = \frac{-5}{9}$
\item $$\begin{array}{rl}2x - 3y &= -2 \\ 1x - 1y &= -2\end{array}$$ \\@$x = -4, y = -2$
\item $$\begin{array}{rl}3x - 5y &= -5 \\ -4x + 4y &= 6\end{array}$$ \\@$x = \frac{-5}{4}, y = \frac{1}{4}$
\item $$\begin{array}{rl}5x - 4y &= -7 \\ -4x + 3y &= 6\end{array}$$ \\@$x = -3, y = -2$
\item $$\begin{array}{rl}3x - 1y &= 4 \\ 2x + 2y &= 4\end{array}$$ \\@$x = \frac{3}{2}, y = \frac{1}{2}$
\item $$\begin{array}{rl}2x + 4y &= 7 \\ 1x + 4y &= 2\end{array}$$ \\@$x = 5, y = \frac{-3}{4}$
\end{enumerate}
\end{multicols}

\newpage

\begin{figure}[ht!]
\vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg}
\end{figure}

\vspace{-15mm}\begingroup
\centering
\LARGE Simultaneous Equations \\[0.5em]
\endgroup

\fontsize{12pt}{16pt}\selectfont
\subsection{Exercise 3. Solve for $x$ and $y$..}
\begin{multicols}{2}
\begin{enumerate}[label=\arabic*)]
\setlength\itemsep{2em}
\item $$\begin{array}{rl}-3x + 7y &= -5 \\ 1x - 1y &= 1\end{array}$$ \\@$x = \frac{1}{2}, y = \frac{-1}{2}$
\item $$\begin{array}{rl}-1x + 4y &= 1 \\ -2x + 2y &= -7\end{array}$$ \\@$x = 5, y = \frac{3}{2}$
\item $$\begin{array}{rl}-3x - 5y &= 6 \\ 2x + 4y &= -3\end{array}$$ \\@$x = \frac{-9}{2}, y = \frac{3}{2}$
\item $$\begin{array}{rl}1x + 3y &= 1 \\ 4x + 5y &= 3\end{array}$$ \\@$x = \frac{4}{7}, y = \frac{1}{7}$
\item $$\begin{array}{rl}2x + 3y &= -5 \\ 1x - 3y &= -7\end{array}$$ \\@$x = -4, y = 1$
\item $$\begin{array}{rl}7x - 5y &= -2 \\ -5x + 3y &= 2\end{array}$$ \\@$x = -1, y = -1$
\item $$\begin{array}{rl}8x - 8y &= 3 \\ 7x - 8y &= 2\end{array}$$ \\@$x = 1, y = \frac{5}{8}$
\item $$\begin{array}{rl}3x + 8y &= -1 \\ -1x - 4y &= -1\end{array}$$ \\@$x = -3, y = 1$
\item $$\begin{array}{rl}1x + 5y &= 3 \\ -2x - 6y &= -2\end{array}$$ \\@$x = -2, y = 1$
\item $$\begin{array}{rl}5x + 6y &= 6 \\ -4x - 3y &= -6\end{array}$$ \\@$x = 2, y = \frac{-2}{3}$
\item $$\begin{array}{rl}5x - 6y &= 1 \\ 8x - 8y &= 2\end{array}$$ \\@$x = \frac{1}{2}, y = \frac{1}{4}$
\item $$\begin{array}{rl}-3x + 7y &= -5 \\ -2x + 2y &= -1\end{array}$$ \\@$x = \frac{-3}{8}, y = \frac{-7}{8}$
\item $$\begin{array}{rl}7x + 4y &= 5 \\ 6x + 3y &= 3\end{array}$$ \\@$x = -1, y = 3$
\item $$\begin{array}{rl}1x + 3y &= 2 \\ -1x + 6y &= -1\end{array}$$ \\@$x = \frac{5}{3}, y = \frac{1}{9}$
\item $$\begin{array}{rl}-5x - 1y &= 3 \\ -4x - 1y &= 2\end{array}$$ \\@$x = -1, y = 2$
\item $$\begin{array}{rl}4x + 2y &= -1 \\ -1x + 1y &= -1\end{array}$$ \\@$x = \frac{1}{6}, y = \frac{-5}{6}$
\item $$\begin{array}{rl}7x + 4y &= -4 \\ 4x + 1y &= -2\end{array}$$ \\@$x = \frac{-4}{9}, y = \frac{-2}{9}$
\item $$\begin{array}{rl}-1x + 1y &= 4 \\ 1x + 3y &= 4\end{array}$$ \\@$x = -2, y = 2$
\item $$\begin{array}{rl}3x + 5y &= 4 \\ -1x - 1y &= 1\end{array}$$ \\@$x = \frac{-9}{2}, y = \frac{7}{2}$
\item $$\begin{array}{rl}-2x - 3y &= -2 \\ 6x + 7y &= 8\end{array}$$ \\@$x = \frac{5}{2}, y = -1$
\end{enumerate}
\end{multicols}

\newpage

\begin{figure}[ht!]
\vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg}
\end{figure}

\vspace{-15mm}\begingroup
\centering
\LARGE Simultaneous Equations \\[0.5em]
\endgroup

\fontsize{12pt}{16pt}\selectfont
\subsection{Exercise 4. Solve for $x$ and $y$..}
\begin{multicols}{2}
\begin{enumerate}[label=\arabic*)]
\setlength\itemsep{2em}
\item $$\begin{array}{rl}3x - 3y &= -6 \\ -1x + 4y &= 4\end{array}$$ \\@$x = \frac{-4}{3}, y = \frac{2}{3}$
\item $$\begin{array}{rl}-2x + 1y &= -3 \\ -1x + 3y &= 1\end{array}$$ \\@$x = 2, y = 1$
\item $$\begin{array}{rl}2x + 4y &= 8 \\ -1x + 2y &= -5\end{array}$$ \\@$x = \frac{9}{2}, y = \frac{-1}{4}$
\item $$\begin{array}{rl}7x - 4y &= -1 \\ -8x + 5y &= 2\end{array}$$ \\@$x = 1, y = 2$
\item $$\begin{array}{rl}-6x + 4y &= 6 \\ 5x - 2y &= -4\end{array}$$ \\@$x = \frac{-1}{2}, y = \frac{3}{4}$
\item $$\begin{array}{rl}-2x - 4y &= 7 \\ 1x + 5y &= -7\end{array}$$ \\@$x = \frac{-7}{6}, y = \frac{-7}{6}$
\item $$\begin{array}{rl}1x - 1y &= -2 \\ 7x - 6y &= -6\end{array}$$ \\@$x = 6, y = 8$
\item $$\begin{array}{rl}2x - 3y &= -3 \\ 5x - 4y &= -3\end{array}$$ \\@$x = \frac{3}{7}, y = \frac{9}{7}$
\item $$\begin{array}{rl}2x + 6y &= -1 \\ -2x - 4y &= 4\end{array}$$ \\@$x = -5, y = \frac{3}{2}$
\item $$\begin{array}{rl}-2x - 4y &= -6 \\ 3x + 7y &= 7\end{array}$$ \\@$x = 7, y = -2$
\item $$\begin{array}{rl}3x - 4y &= 4 \\ 3x - 6y &= 7\end{array}$$ \\@$x = \frac{-2}{3}, y = \frac{-3}{2}$
\item $$\begin{array}{rl}4x + 6y &= -5 \\ -1x - 2y &= 3\end{array}$$ \\@$x = 4, y = \frac{-7}{2}$
\item $$\begin{array}{rl}5x + 1y &= -3 \\ 7x + 3y &= -3\end{array}$$ \\@$x = \frac{-3}{4}, y = \frac{3}{4}$
\item $$\begin{array}{rl}1x - 3y &= 1 \\ -2x + 5y &= -1\end{array}$$ \\@$x = -2, y = -1$
\item $$\begin{array}{rl}6x + 6y &= 4 \\ 3x + 2y &= 3\end{array}$$ \\@$x = \frac{5}{3}, y = -1$
\item $$\begin{array}{rl}3x + 5y &= 6 \\ -4x - 5y &= -5\end{array}$$ \\@$x = -1, y = \frac{9}{5}$
\item $$\begin{array}{rl}-3x + 3y &= 5 \\ 4x - 2y &= -8\end{array}$$ \\@$x = \frac{-7}{3}, y = \frac{-2}{3}$
\item $$\begin{array}{rl}-2x - 6y &= -2 \\ -1x - 7y &= -2\end{array}$$ \\@$x = \frac{1}{4}, y = \frac{1}{4}$
\item $$\begin{array}{rl}-5x + 1y &= -2 \\ 8x - 3y &= 3\end{array}$$ \\@$x = \frac{3}{7}, y = \frac{1}{7}$
\item $$\begin{array}{rl}5x - 6y &= 7 \\ -5x + 7y &= -8\end{array}$$ \\@$x = \frac{1}{5}, y = -1$
\end{enumerate}
\end{multicols}

\newpage

\begin{figure}[ht!]
\vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg}
\end{figure}

\vspace{-15mm}\begingroup
\centering
\LARGE Simultaneous Equations \\[0.5em]
\endgroup

\fontsize{12pt}{16pt}\selectfont
\subsection{Exercise 5. Solve for $x$ and $y$..}
\begin{multicols}{2}
\begin{enumerate}[label=\arabic*)]
\setlength\itemsep{2em}
\item $$\begin{array}{rl}7x + 1y &= -4 \\ 5x + 1y &= -2\end{array}$$ \\@$x = -1, y = 3$
\item $$\begin{array}{rl}5x + 7y &= -7 \\ 2x + 1y &= -2\end{array}$$ \\@$x = \frac{-7}{9}, y = \frac{-4}{9}$
\item $$\begin{array}{rl}-6x - 6y &= -1 \\ 5x + 6y &= 2\end{array}$$ \\@$x = -1, y = \frac{7}{6}$
\item $$\begin{array}{rl}-1x - 2y &= 1 \\ -3x - 4y &= 6\end{array}$$ \\@$x = -4, y = \frac{3}{2}$
\item $$\begin{array}{rl}-5x + 7y &= 4 \\ 3x - 4y &= -1\end{array}$$ \\@$x = 9, y = 7$
\item $$\begin{array}{rl}3x - 4y &= 4 \\ -3x + 2y &= -3\end{array}$$ \\@$x = \frac{2}{3}, y = \frac{-1}{2}$
\item $$\begin{array}{rl}2x - 5y &= 2 \\ 5x - 8y &= 3\end{array}$$ \\@$x = \frac{-1}{9}, y = \frac{-4}{9}$
\item $$\begin{array}{rl}-2x + 2y &= 6 \\ -4x + 3y &= 8\end{array}$$ \\@$x = 1, y = 4$
\item $$\begin{array}{rl}-1x + 7y &= -8 \\ -2x + 6y &= -7\end{array}$$ \\@$x = \frac{1}{8}, y = \frac{-9}{8}$
\item $$\begin{array}{rl}6x - 1y &= 8 \\ -2x + 1y &= -3\end{array}$$ \\@$x = \frac{5}{4}, y = \frac{-1}{2}$
\item $$\begin{array}{rl}5x + 3y &= 8 \\ -2x - 2y &= -5\end{array}$$ \\@$x = \frac{1}{4}, y = \frac{9}{4}$
\item $$\begin{array}{rl}-2x - 6y &= 2 \\ -1x - 6y &= -1\end{array}$$ \\@$x = -3, y = \frac{2}{3}$
\item $$\begin{array}{rl}4x + 8y &= 5 \\ -1x - 4y &= -2\end{array}$$ \\@$x = \frac{1}{2}, y = \frac{3}{8}$
\item $$\begin{array}{rl}-1x + 6y &= 5 \\ -2x + 4y &= 6\end{array}$$ \\@$x = -2, y = \frac{1}{2}$
\item $$\begin{array}{rl}-8x - 6y &= -8 \\ 5x + 4y &= 6\end{array}$$ \\@$x = -2, y = 4$
\item $$\begin{array}{rl}6x + 5y &= -6 \\ -8x - 6y &= 7\end{array}$$ \\@$x = \frac{1}{4}, y = \frac{-3}{2}$
\item $$\begin{array}{rl}-4x + 6y &= -2 \\ 5x - 7y &= 1\end{array}$$ \\@$x = -4, y = -3$
\item $$\begin{array}{rl}1x - 7y &= -1 \\ 2x - 7y &= 1\end{array}$$ \\@$x = 2, y = \frac{3}{7}$
\item $$\begin{array}{rl}1x + 2y &= 1 \\ -7x - 8y &= -3\end{array}$$ \\@$x = \frac{-1}{3}, y = \frac{2}{3}$
\item $$\begin{array}{rl}-8x + 7y &= 8 \\ -7x + 5y &= 6\end{array}$$ \\@$x = \frac{-2}{9}, y = \frac{8}{9}$
\end{enumerate}
\end{multicols}

\newpage

\begin{figure}[ht!]
\vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg}
\end{figure}

\vspace{-15mm}\begingroup
\centering
\LARGE Simultaneous Equations \\[0.5em]
\endgroup

\fontsize{12pt}{16pt}\selectfont
\subsection{Exercise 6. Solve for $x$ and $y$..}
\begin{multicols}{2}
\begin{enumerate}[label=\arabic*)]
\setlength\itemsep{2em}