Solve the system of equations by elimination :
3X - 9Y = 5
6X + 2Y = 18

The correct answer is: x = 43 over 15 and y=8 over 20

Complete step by step solution:
Let 3x-9y=5…(i)
and 6x+ 2y=18….(ii)
On multiplying (i) with 2, we get 2(3x - 9y = 5)
⇒ 6x - 18y = 10…(iii)
Now, we have the coefficients of x in (ii) and (iii) to be the same.
On subtracting (iii) from (ii),
we get LHS to be 6x + 2y-(6x - 18y) = 2y - (- 18y) = 20y
and RHS to be 18 - 10 = 8
On equating LHS and RHS, we have 20y = 8
⇒ y = 
On substituting the value of y in (i), we get 3x - 9 ×  =5

 ⇒ 3x -  =5

⇒ 3x = 5 + 

⇒ 3x =  = 

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