## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$x=\dfrac{1}{5}, y = \dfrac{3}{10} \text{ or } \left(\dfrac{1}{5}, \dfrac{3}{10}\right)$
The system of equations is given by the following two equations: \begin{cases} 3x-2y=0\hspace{20pt} (1)\3mm] 5x+10y=4 \hspace{20pt} (2) \end{cases} Multiplying equation (1) by 5 so that the coefficients of y in the two equations are additive inverses gives: 15x-10y=0\hspace{20pt} (1) \text{Add the two equations to eliminate } y: \[ \begin{aligned} 15x-10y&=0 \\[2mm] 5x+10y&=4 \ \\[3mm] \hline 20x&=4\\[2mm] \end{aligned} Divdei both sides by $20$ to obtain: $x=\dfrac{4}{20}$ $x=\dfrac{1}{5}$ $\text{Substituting in equation (2) for }x=\dfrac{1}{5}$ gives: $5\left(\dfrac{1}{5} \right)+10y = 4$ $1+10y=4$ $10y = 3$ $y = \dfrac{3}{10}$ Therefore, the solution is: $\boxed{x=\dfrac{1}{5} \hspace{20pt} y = \dfrac{3}{10}}$