Solve the system of equations by elimination :
X + 3Y = 7
2X + 2Y = 6

The correct answer is: We can also solve these system of equations by making the coefficients of y to be the same in both the equations.

Complete step by step solution:
Let x + 3y = 7…(i)
and 2x + 2y = 6…(ii)
On multiplying (i) with 2, we get 2(x + 3y = 7)
⇒ 2x + 6y = 14…(iii)
Now, we have the coefficients of  in (ii) and (iii) to be the same.
On subtracting (ii) from (iii),
we get LHS to be 2x + 6y - (2x + 2y) = 6y - 2y = 4y
and RHS to be 14 - 6 = 8
On equating LHS and RHS, we have 4y = 8
⇒ y = 2
On substituting the value of y in (i), we get x + 3×2 = 7
⇒ x + 6 = 7
⇒ x = 1
Hence we get x = 1 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.