Question

If 19x - 17y= 55 and 17x – 19y=53, then the value of x - y is:​

Answer 1

Answer: 3

Step-by-step explanation:

19x  -17y= 55

multiplying 17 on both side

323x - 289y = 935 .......................(1)

17x-19y= 53

multiplying 19 on both side

323x - 361y = 1007 ......................(2)

(1)-(2),

72y=-72

y=-1

and x=2

Therefore x-y= 2-(-1)= 3

Answer 2

Given: The equations 19x - 17y= 55 and 17x-19y=53

To find: Value of x-y

Solution: When two linear equations consisting of two variables are given, value of a variable can be found by making the coefficient of other variable same in both equations and cancelling it.

Here,

19x-17y=55 -----equation (i)

17x-19y =53 -----equation (ii)

For finding x, we make the coefficient of y same in both the equations.

We multiply equation (i) by 19 and equation (ii) by 17 to make the coefficient of y same.

The equations now become:

361x-323y= 1045 -----equation (iii)

289x-323y= 901----equation(iv)

Subtracting equation (iv) from equation (iii),

72x = 144

=> x = 144/72

=> x = 2

Putting x=2 in equation (i),

19×2-17y=55

=>38-17y = 55

=> -17y = 55-38

=> -17y = 17

=> -y = 17/17

=> y = -1

Therefore,

x-y

= 2-(-1)

=2+1

=3

Therefore, the value of x-y is 3.