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

The correct answer is: x = 3 and y = - 1

Complete step by step solution:
Let x - y = 4…(i)
and 2x + y = 5….(ii)
On multiplying (i) with 2, we get 2( x - y = 4)
⇒ 2x - 2y = 8…(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 - 2y - (2x + y) = - 2y - y = - 3y
and RHS to be 8 - 5 = 3
On equating LHS and RHS, we have - 3y = 3
⇒ y = - 1
On substituting the value of  in (i), we get - (- 1) = 4

⇒x + 1 = 4

⇒x = 4 - 1

⇒x = 3
Hence we get x = 3 and y = - 1
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations.