Answer
$x=1$
$y=-2$
Work Step by Step
$\begin{cases} 3x+y=1\\5x+2y=1\end{cases}$
Let $3x+y=1$ be equation 1 and $5x+2y=1$ be equation 2
Solve for $y$ in equation 1:
$3x+y=1$
$y=1-3x$
Let this equation be equation 3
Substitute equation 3 in equation 2:
$5x+2y=1$
$5x+2(1-3x)=1$
Simplify and solve for $x$:
$5x+2-6x=1$
$-x=-1$
$x=1$
Finally, substitute $x=1$ in equation 3:
$y=1-3x$
$y=1-3(1)=-2$