Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 14

Decide whether the ordered pair $(5,2)$ is a solution of the system $
\begin{equation}
\begin{aligned}

2x - y =& 8 \\
3x + 2y =& 20

\end{aligned}
\end{equation}
$.

We substitute the ordered pair to the equations

Equation 1


$
\begin{equation}
\begin{aligned}

2x - y =& 8
&& \text{Given equation}
\\
2(5) - 2 =& 8
&& \text{Substitute $x = 5$ and $y = 2$}
\\
8 =& 8
&&

\end{aligned}
\end{equation}
$


Equation 2


$
\begin{equation}
\begin{aligned}

3x + 2y =& 20
&& \text{Given equation}
\\
3(5) + 2(2) =& 20
&& \text{Substitute $x = 5$ and $y = 2$}
\\
15 + 4 =& 20
&&
\\
19 =& 20
&&

\end{aligned}
\end{equation}
$


The ordered pair $(5,2)$ is not the solution of the system.