Question

solve 99x+101y = 499,101x+99y = 501

Answer 1

Given 
99x+101y = 499------------> 1
101x+99y = 501-----------------> 2 
multiply equation 1 with 101 
then we get  (99x+101y = 499)101
⇒9999x+10201y=50399----------------> 3
Now let us consider 2nd equation 
multiply 2nd equation by 99 
then we get (101x+99y = 501)99
⇒9999x+9801y=49599---------------> 4
solving 3 & 4 we get 

400y = 800
⇒y = 2 
Now substitute y = 2 in equation 1 
then we get the value of x 
99x+101*2=499
99x+202=499
99x=297
x=3

Answer 2

Answer:

Given

99x+101y = 499------------> 1

101x+99y = 501-----------------> 2

multiply equation 1 with 101

then we get (99x+101y = 499)101

⇒9999x+10201y=50399----------------> 3

Now let us consider 2nd equation

multiply 2nd equation by 99

then we get (101x+99y = 501)99

⇒9999x+9801y=49599---------------> 4

solving 3 & 4 we get

400y = 800

⇒y = 2

Now substitute y = 2 in equation 1

then we get the value of x

99x+101*2=499

99x+202=499

99x=297

x=3