Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 78

For each system, $
\begin{equation}
\begin{aligned}

6x + y =& 5 \\
-x + y =& -9

\end{aligned}
\end{equation}
$


(a) Solve by elimination or substitution method.

Using Elimination Method


$
\begin{equation}
\begin{aligned}

6x + y =& 5 && \\
x - y =& 9 && -1 \times \text{ Equation 2} \\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

7x \phantom{+y} =& 14
&& \text{Add}
\\
x =& 2
&& \text{Divide each side by $7$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

6(2) + y =& 5
&& \text{Substitute $x = 2$ in Equation 1}
\\
12 + y =& 5
&& \text{Multiply}
\\
y =& -7
&& \text{Subtract each side by $12$}

\end{aligned}
\end{equation}
$



(b) Graph then solve each equation for $y$ first.

Equation 1


$
\begin{equation}
\begin{aligned}

& 6x + y = 5
&& \text{Given equation}
\\
& y = -6x + 5
&& \text{Subtract each side by $6x$}

\end{aligned}
\end{equation}
$


Equation 2


$
\begin{equation}
\begin{aligned}

-x + y =& -9
&& \text{Given equation}
\\
y =& x - 9
&& \text{Add each side by $x$}

\end{aligned}
\end{equation}
$