Question

solve x and y :99x+101y=99; 101x+99y=101

Answer 1

99x + 101y = 99 ----> [1 ]
101x + 99y = 101 ----> [2 ]

Adding 1 and 2 ,

99x + 101x + 101y + 99y = 99 + 101

200x + 200y = 200

----> dividing by 200 on lhs and rhs

x + y = 1 ----> [3]


Now subtract equation 1 from 2

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

dividing by 2 on lhs and rhs ,

x - y = 1 ----->[4]


Adding equations 3 and 4 ,

x + y = 1
x - y = 1
--------------

2x = 2

x = 1


x - y = 1

1 - y = 1

1 - 1 = y

y = 0

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x = 1 , y = 0

Answer 2

Given:
99x + 101y = 99 ------(1)
101x + 99y = 101 --------(2)

subtract equation (2) to equation (1)

(101x + 99y )- (99x + 101y) = 101 - 99
(101 - 99)x + (99 - 101)y = 2
2x - 2y = 2
x - y = 1
x = y + 1 put this in equation (1)

99(y +1) + 101y = 99
99y + 99 + 101y = 99
y = 0 so, x = 0 + 1 = 1

hence, x = 1 and y = 0