Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Mixed Review - Page 858: 47

$x=0; y=\dfrac{4}{5}$

Since we are given two equations $12x+5y=4$ and $3x-10y=-8$ Now, multiply the equation $1x+5y=4$ by $2$. we have $24x+10y=8$ and $3x-10y=-8$ After solving, we get $27 x=0 \implies x=0$ Then, $3(0)-10y=-8$ This implies $ y=\dfrac{-8}{-10}=\dfrac{4}{5}$ Hence, $x=0; y=\dfrac{4}{5}$