Solve the system of equations by elimination :
3X - 7Y = 16
5X - 4Y = 19

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 3x - 7y = 16…(i)
and 5x - 4y = 19….(ii)
On multiplying (i) with 5, we get 5(3x - 7y = 16)
⇒15x - 35y = 80…(iii)
On multiplying (ii) with 3, we get 3(5x - 4y = 19)
⇒15x - 12y = 57…(iv)
Now, we have the coefficients of x in (iii) and (iv) to be the same.
On subtracting (iv) from (iii),
we get LHS to be 15x - 35y - (15x - 12y) =  -35y+ 12y= - 23y
and RHS to be 80 - 57 = 23
On equating LHS and RHS, we have - 23y = 23
⇒ y = - 1
On substituting the value of  in (i), we get 3x - 7× - 1 = 16
⇒ 3x + 7 = 16
⇒ 3x = 16 - 7
⇒ 3x = 9
⇒ x = 3
Hence we get = 3 and y = - 1
Note: We can also solve these system of equations by making the coefficients ofto be the same in both the equations.