Solve the system of equations by elimination :
3X + 2Y = 8
X + 4Y = - 4

The correct answer is: we get x = 4 and y = - 2

Complete step by step solution:
Let 3x + 2y = 8…(i)
and x + 4y = - 4….(ii)
On multiplying (ii) with 3, we get 3(x + 4y=-4)
⇒3x + 12y = - 12…(iii)
Now, we have the coefficients of  in (i) and (iii) to be the same.
On subtracting (i) from (iii),
we get LHS to be 3x + 12y - (3x + 2y) = 12y - 2y = 10y
and RHS to be - 12 - 8 = - 20
On equating LHS and RHS, we have 10y = - 20
⇒y = - 2
On substituting the value of y in (i), we get 3x + 2× - 2 = 8
⇒ 3x - 4 = 8
⇒ 3x = 8 + 4
⇒ 3x = 12
⇒x = 4
Hence we get x = 4 and y = - 2
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations