Answer
The values of x and y for the given system $3x+5y=-2$ and $2x+3y=0$ are $x=6\,\,\text{ and }\,\,y=-4$.
Work Step by Step
$3x+5y=-2$ ( $1$ )
$2x+3y=0$ ( $2$ )
And multiply $-2$ on the both sides of the first equation:
$\begin{align}
& 3x+5y=-2 \\
& -2\left( 3x+5y \right)=-2\cdot -2
\end{align}$
$-6x-10y=4$ (a)
And multiply by $3$ on the both sides of the second equation
$\begin{align}
& 2x+3y=0 \\
& 3\left( 2x+3y \right)=0\cdot 3
\end{align}$
$6x+9y=0$ (b)
Add (a) and (b):
$\begin{align}
& -6x-10y+6x+9y=4+0 \\
& -y=4 \\
& y=-4
\end{align}$
And to obtain the value of x, substitute the value $y=-4$ in (b):
$\begin{align}
& 6x+9\cdot -4=0 \\
& 6x-36=0
\end{align}$
Add 36 both sides:
$\begin{align}
& 6x-36+36=0+36 \\
& 6x=36
\end{align}$
And multiply both sides by $\frac{1}{6}$
$\begin{align}
& \frac{1}{6}\cdot 6x=\frac{1}{6}\cdot 36 \\
& x=6 \\
\end{align}$
Hence, the values of x and y for the given system $3x+5y=-2$ and $2x+3y=0$ are $x=6\,\,\text{ and }\,\,y=-4$.
