Solve :

3x + 2y = 14

-x + 4y = 7

3x + 2y = 14 …………… (1)

-x + 4y = 7 …………… (2)

Multiply 1 in the first equation and 3 in the second equation, then add both equations.

(3x + 2y = 14) x 1

(-x + 4y = 7) x 3

$\begin{matrix} & 3x & + & 2y & = & 14 \ & -3x & + & 12y & = & 21 \ \hline & & & 14y & = & 14 + 21 \ \Rightarrow & & & 14y & = & 35 \end{matrix}$

⇒ y = $\dfrac{35}{14}$

⇒ y = 2.5

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

⇒ 3x + 2 $\times$ 2.5 = 14

⇒ 3x + 5 = 14

⇒ 3x = 14 - 5

⇒ 3x = 9

⇒ x = $\dfrac{9}{3}$

⇒ x = 3

Hence, the value of x = 3 and y = 2.5.