Question

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

Answer 1

Answer :

First Add Both Equations

99x + 101y = 499

101x + 99y = 501

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200x+200y=1000

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Taking 200 common from the equation

Therefore x+y=5 .......(i)

Substract one equation from other

99x + 101y = 499

(-) 101x + 99y = 501

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- 2x + 2y = -2

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Taking 2 as common

Therefore -x+y=-1 ........(ii)

Equating (i) and (ii)

x + y = 5

-x + y = -1

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2y=4

y = 2

x = 3

Answer 2

Here is your answer

99x+ 101y =499 ----(I)
101x+ 99y= 501 ----(ii)

adding I and ii
200x+ 200y= 1000
200(x+y) = 1000
x+y = 1000/200
x+y = 5 -----(iii)

subtracting eq I from ii
2x-2y = 2
x- y = 1 -----(iv)

from eq iii and iv
2x= 6
x=3

putting x=3 in eq iii
3+y= 5
y= 5-3=2

so, x= 3 and y= 2

Hope it is useful