Solve the following system of equations by elimination :
4X + 3Y = 6
2X - 5Y = 16

The correct answer is: x = 3 and y = - 2

Complete step by step solution:
Let 4x+ 3y=6…(i)
and 2x - 5y = 16…(ii)
On multiplying (ii) with 2, we get 2(2x - 5y = 16)

                                      ⇒ 4x - 10y = 32…(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 4x - 10y - (4x + 3y) = - 10y - 3y = - 13y
and RHS to be 32 - 6 = 26
On equating LHS and RHS, we have  - 13y = 26

                                                     ⇒ y = - 2
On substituting the value of y in (i), we get 4x + 3× - 2 = 6

                                                     ⇒ 4x - 6 = 6

                                                     ⇒ 4x = 12

                                                      ⇒ x = 3
Hence we get x = 3 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.