Solve the system of equations by elimination :
Y = X + 13
2X + 7Y = 10

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 y=x+ 13
⇒ x - y= - 13…(i)
and 2x + 7y = 10…(ii)
On multiplying (i) with 2, we get 2(x – y = - 13)
⇒ 2x - 2y = - 26…(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 + 7y) = - 2y - 7y = - 9y
and RHS to be – 26 -10 = - 36
On equating LHS and RHS, we have - 9y = - 36
⇒ y = 4
On substituting the value of y in (i), we get x – 4 = - 13
⇒ x = - 13 + 4
⇒ x = - 9
Hence we get x = - 9 and y = 4
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations.