Solve the system of equations by elimination :
6X + 12Y = - 6
3X - 2Y = - 27

The correct answer is: We can also solve these system of equations by making the coefficients of to be the same in both the equations.

Complete step by step solution:
Let 6x + 12y = - 6…(i)
and 3x - 2y = - 27…(ii)
On multiplying (ii) with 2, we get 2(3x - 2y = - 27)
⇒ 6x - 4y = - 54…(iii)
Now, we have the coefficients of  in (i) and (iii) to be the same.
On subtracting (iii) from (i),
we get LHS to be 6x + 12y - (6x - 4y) = 12y + 4y = 16y
and RHS to be - 6 - (- 54) = 48
On equating LHS and RHS, we have 16y = 48
⇒ y = 3
On substituting the value of  in (i), we get 6x + 12×3 = - 6
⇒ 6x + 36 = - 6
⇒ 6x = - 6 - 36
⇒ 6x = - 42
⇒ x = - 7
Hence we get x = - 7 and y = 3
Note: We can also solve these system of equations by making the coefficients of
to be the same in both the equations.