Beginning Algebra With Applications, Chapter 6, 6.2, Section 6.2, Problem 64

Solve the system of equations: $\begin{equation} \begin{aligned} 1.25x - 0.01y =& 1.5 \\ 0.24x - 0.02y =& -1.52 \end{aligned} \end{equation}$


$\begin{equation} \begin{aligned} 0.24x - 0.02y =& -1.52 \qquad \text{Solve equation 2 for } y \\ \\ -0.02y =& -0.24x - 1.52 \\ \\ y =& \frac{-0.24x - 1.52}{-0.02} \\ \\ y =& 12x+76 \end{aligned} \end{equation}$




$\begin{equation} \begin{aligned} 1.25x - 0.01y =& 1.5 \qquad \text{Substitute } 12x+76 \text{ for $y$ in equation 1} \\ \\ 1.25x-0.01 (12x+76) =& 1.5 \\ \\ 1.25x - 0.12x - 0.76 =& 1.5 \\ \\ 1.13x =& 1.5+0.76 \\ \\ 1.13x =& 2.26 \\ \\ x =& 2 \end{aligned} \end{equation}$


Substitute the value of $x$ in equation 2


$\begin{equation} \begin{aligned} y =& 12(2) + 76 \\ \\ y =& 24+76 \\ \\ y =& 100 \end{aligned} \end{equation}$


The solution is $(2,100)$.