Solve :

3x-5y+1=0
2x-y+3=0

3x - 5y = -1 …………… (1)

2x - y = -3 …………… (2)

Multiply 2 in the first equation and 3 in the second equation, then subtract both equations.

(3x - 5y = -1) x 2

(2x - y = -3) x 3

$\begin{matrix} & 6x & - & 10y & = & -2 \ & 6x & - & 3y & = & -9 \ & - & + & & & + \ \hline & & - & 7y & = & -2 + 9 \ \Rightarrow & & - & 7y & = & 7 \end{matrix}$

⇒ y = -$\dfrac{7}{7}$

⇒ y = - 1

Substituting the value of y in equation (1), we get:

⇒ 3x - 5 $\times$ (-1) = -1

⇒ 3x + 5 = -1

⇒ 3x = -1 - 5

⇒ 3x = -6

⇒ x = -$\dfrac{6}{3}$

⇒ y = - 2

Hence, the value of x = -2 and y = -1.