Beginning Algebra With Applications, Chapter 6, 6.2, Section 6.2, Problem 60

Solve the system of equations: $\begin{equation} \begin{aligned} 0.8x-0.1y =& 0.3 \\ 0.5x - 0.2y =& -0.5 \end{aligned} \end{equation}$


$\begin{equation} \begin{aligned} 0.5x -0.2y =& -0.5 \qquad \text{Solve equation 2 for } x \\ \\ 0.5x =& 0.2y - 0.5 \\ \\ x =& \frac{0.2y - 0.5}{0.5} \\ \\ x =& \frac{0.2}{0.5} y - 1 \end{aligned} \end{equation}$




$\begin{equation} \begin{aligned} 0.8x - 0.1y =& 0.3 \qquad \text{Substitute } \frac{0.2}{0.5}y-1 \text{ for $x$ in equation 1} \\ \\ 0.8 \left( \frac{0.2}{0.5} y - 1 \right) - 0.1y =& 0.3 \\ \\ \frac{0.16}{0.5} y - 0.8 - 0.1y =& 0.3 \\ \\ 0.32y - 0.1y =& 0.3+0.8 \\ \\ 0.22y =& 1.1 \\ \\ y =& 5 \end{aligned} \end{equation}$


Substitute the value of $y$ in equation 2


$\begin{equation} \begin{aligned} x =& \frac{0.2}{0.5} y - 1 \\ \\ x =& \frac{0.2}{0.5} (5) - 1 \\ \\ x =& 2-1 \\ \\ x =& 1 \end{aligned} \end{equation}$


The solution is $(1,5)$.