Solve the system of equations by elimination :
X - 2Y = 1
2X + 3Y= - 12

The correct answer is: x = - 3 and y = - 2

Complete step by step solution:
Let x - 2y = 1…(i)
and 2x + 3y=-12….(ii)
On multiplying (i) with 2, we get 2(x - 2y = 1)
⇒ 2x - 4y = 2…(iii)
Now, we have the coefficients of x in (ii) and (iii) to be the same.
On subtracting (ii) from (iii),
we get LHS to be 2x - 4y - (2x + 3y) = - 4y - 3y = - 7y
and RHS to be 2 - (- 12) = 14
On equating LHS and RHS, we have - 7y = 14
⇒ y = - 2
On substituting the value of y in (i), we get x - 2 × - 2 =1
⇒ x + 4 = 1
⇒ x = 1-4
⇒ x = - 3
Hence we get x = - 3 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