Solve :

12x + 15y + 18 = 0

18x - 7y + 86 = 0

12x + 15y + 18 = 0 …………… (1)

18x - 7y + 86 = 0 …………… (2)

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

(12x + 15y = -18) x 3

(18x - 7y = -86) x 2

$\begin{matrix} & 36x & + & 45y & = & -54 \ & 36x & - & 14y & = & -172 \ & - & + & & & + \ \hline & & & 59y & = & -54 + 172 \ \Rightarrow & & & 59y & = & 118 \end{matrix}$

⇒ y = $\dfrac{118}{59}$

⇒ y = 2

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

⇒ 12x + 15 $\times$ 2 = -18

⇒ 12x + 30 = -18

⇒ 12x = -18 - 30

⇒ 12x = -48

⇒ x = -$\dfrac{48}{12}$

⇒ x = -4

Hence, the value of x = -4 and y = 2.