Solve the system of equations by elimination :
8X - 2Y = - 8
5X - 4Y = 17

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 8x - 2y = - 8…(i)
and 5x - 4y = 17…(ii)
On multiplying (i) with 2, we get 2(8x - 2y = - 8)
⇒16x - 4y = -16…(iii)
Now, we have the coefficients of y in (ii) and (iii) to be the same.
On subtracting (iii) from (ii),
we get LHS to be 5x - 4y - (16x - 4y) = 5x - 16x = - 11x
and RHS to be 17 - (- 16) = 33
On equating LHS and RHS, we have - 11x = 33
⇒ x = - 3
On substituting the value of  in (i), we get 8× - 3 - 2y = - 8
⇒ - 24 - 2y = - 8
⇒ - 2y = - 8 + 24
⇒ - 2y = 16
⇒ y = - 8
Hence we get x = - 3 and y = - 8
Note: We can also solve these system of equations by making the coefficients of
to be the same in both the equations.