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.