Solve the system of equations by elimination :
7X - 4Y = - 12
X - 2Y = 4

The correct answer is: x = - 4 and y = - 4

Complete step by step solution:
Let 7x - 4y = - 12…(i)
and x - 2y = 4….(ii)
On multiplying (ii) with 7, we get 7( x - 2y = 4)
⇒7x - 14y = 28…(iii)
Now, we have the coefficients of x in (i) and (iii) to be the same.
On subtracting (i) from (iii),
we get LHS to be 7x - 14y - (7x - 4y) = - 14y + 4y = - 10y
and RHS to be 28- (- 12) = 40
On equating LHS and RHS, we have - 10y = 40
⇒ y = - 4
On substituting the value of y in (ii), we get x - 2 × - 4 = 4

⇒x + 8 = 4

⇒x = 4 - 8

⇒ x = - 4
Hence we get x = - 4 and y = - 4
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations.