3X - 2Y = 38
X = 6 - Y

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 - 2y = 38…(i)
and x = 6 - y
⇒ x + y = 6…(ii)
On multiplying (ii) with 3, we get 3(x + y=6)
⇒ 3x + 3y = 18…(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 3x + 3y - (3x - 2y) = 3y + 2y = 5y
and RHS to be 18 - (38) = - 20
On equating LHS and RHS, we have 5y = - 20
⇒ y = - 4
On substituting the value of y in (i), we get 3x - 2× - 4 = 38

⇒ 3x + 8 = 38

⇒ 3x = 38 - 8

⇒ 3x = 30

⇒ x = 10
Hence we get x = 10 and y = - 4
Note: We can also solve these system of equations by making the coefficients of
to be the same in both the equations.