Solve :

8x + 13y - 29 = 0

12x - 7y - 17 = 0

8x + 13y - 29 = 0 …………… (1)

12x - 7y - 17 = 0 …………… (2)

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

⇒ (8x + 13y = 29) x 3

(12x - 7y = 17) x 2

$\begin{matrix} & 24x & + & 39y & = & 87 \ & 24x & - & 14y & = & 34 \ & - & + & & & - \ \hline & & & 53y & = & 87 - 34 \ \Rightarrow & & & 53y & = & 53 \end{matrix}$

⇒ y = $\dfrac{53}{53}$

⇒ y = 1

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

⇒ 8x + 13 $\times$ 1 = 29

⇒ 8x + 13 = 29

⇒ 8x = 29 - 13

⇒ 8x = 16

⇒ x = $\dfrac{16}{8}$

⇒ x = 2

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