Solution:

Let’s rewrite the given equations by shifting constant terms to RHS:
3x − 4y = 15 ... (i)
x + y = − 2 ... (ii)

To eliminate x, multiply equation (ii) by 3,
3x + 3y = − 6 ... (iii)

Now, subtract (iii) from (i),

		3x	−	4y	=		15	... (i)
−	⊕	3x	⊕	3y	=	⊖	6	... (iii)
	−		−			+
			−	7y	=		21

  \(\displaystyle y = \frac {21}{- 7}\)

∴ y = − 3 ... (iv)

Substituting the value of y in equation (ii),
  x + y = − 2 ... (ii)
∴ x − 3 = − 2
∴ x = − 2 + 3
∴ x = 1 ... (v)

(1, − 3) is the solution of the above equations.

Thus, we can see that the solution is same even when we solve it by eliminating x.