Solve the system of equations by elimination :
4X - 3Y = 17
2X - 5Y = 5

The correct answer is: x = 5 and y = 1

Complete step by step solution:
Let 4x - 3y = 17…(i)
and 2x - 5y = 5….(ii)
On multiplying (ii) with 2, we get 2(2x - 5y = 5)
⇒4x - 10y = 10…(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 4x - 10y - (4x - 3y)= - 10y + 3y = - 7y
and RHS to be 10 -17 = - 7
On equating LHS and RHS, we have - 7y = - 7
⇒ y = 1
On substituting the value of y in (i), we get 4x - 3 × 1 = 17
⇒4 x - 3 = 17
⇒4x = 17 + 3
⇒4x = 20
⇒x = 5
Hence we get x = 5 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.