Question

19x-17y=55 and 17x-19y=53 then the value of x+y is?

Answer 1

Answer:

The given two equations are:

19x−17y=55

………..(1)

17x−19y=53

………..(2)

We will multiply equation (1)

by 17, we get

(19x−17y)×17=55×17

⇒(19×17)x−172y=55×17

……………………….(3)

We will multiply equation (2)

by 19, we get

(17x−19y)×19=53×19

⇒(17×19)x×192y=53×19

………………………(4)

Hence, subtracting the equations, we get,

Hence, subtracting the equation (4)

from equation (3)

, we get,

[(19×17)x−172y]−[(19×17)x−192y]=55×17−53×19

⇒(19×17)x−172y−(19×17)x+192y=55×17−53×19

Solving the terms with same variables, we get,

⇒(192−172)y=(55×17)−(53×19)

Now, applying the identity (a2−b2)=(a+b)(a−b)

⇒(19+17)(19−17)y=(55×17)−(53×19)

Now, we would transport everything which is multiplying to the variable y

in the LHS to the denominator of RHS.

⇒y=(55×17)−(53×19)(19+17)(19−17)

Now, we would solve this further,

⇒y=935−100736×2

⇒y=−7272

⇒y=−1

Now, substituting this value in the equation,19x−17y=55

, we get,

19x−17(−1)=55

19x+17=55

Subtracting 17 from both sides,

19x=38

Dividing both sides by 19

⇒x=2

Therefore, the required value of x−y

is:

x−y=2−(−1)

⇒x−y=2+1=3

Therefore, if 19x−17y=55

and 17x−19y=53

, then the value of x−y=3