Question

Q.1 Solve the following questions
1. 99x + 10ly = 499 ; 101x + 99y = 501. Find x + y
answer:​

Answer 1

Given that 99x + 101y = 499 … (1)

101x + 99y = 501 … (2)

Adding equations (1) and (2), we get.

200x + 200y = 1000 Or, x + y = 5 … (3)

Subtracting (1) from (2), we get,

2x – 2y = 2 Or, x – y = 1 … (4)

Adding (3) and (4), we get,

2x = 6 x = 3

Putting the value of x in (3),

we get, y = 2

So, x + y = 3 + 2 = 5

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Answer 2

Explanation:

Let,

99x + 101y = 499---------------------------------(equation i)

and

101x + 99y = 501----------------------------------(equation ii)

Multipling equation i with 99 and equation ii with 101 to make the cofficient of y be same, we get

99(99x+101y)=99(499)

=> 9801x+9999y=49401------------------------(equation iii)

101(101x+99y)=101(501)

=> 10201x+9999y=50601-----------------------(equation iv)

Subtracting equation iii from iv

10201x+9999y-(9801x+9999y)=50601-(49401)

=> 10201x+9999y-9801x-9999y=50601-49401

=> 400x=1200

=> x=1200/400

=> x=3

Substituting the value of x in equation iii ,we get

9801x+9999y=49401

9801(3)+9999y=49401

29403+9999y=49401

9999y=49401-29403

9999y=19998

y=19998/9999

y=2

so x+y=3+2=5