Question

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

Answer 1

Hello!!

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Consider,

99x+101y=499_______(1)

101x+99y=501 ________(2)

multiplying equation (1) by -101 we get

-9999x-10201y=-50,399_________(3)

multiplying equation (2) by 99

9999x+9801y=49,599___________(4)

adding (3) and (4) we get

-400y=-800

y=2

substituting y=2 in equation (1) we get

99x+202=499

99x=499-202

99x=297

x=297/99

x=3

CHECK

99(3)+101(2)=297+202=499

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Thanks!!

Answer 2

Heya buddy!!!

Here's the answer to your question...

99x+101y=499 and 101x+99y=501

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

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

subtract (i) from (ii)

2x - 2y = 2 or

x - y =1 or

x = 1 + y......................(iii)

add (i) and (ii)

200x + 200y = 1000 or

x + y = 5......................(iv)

Now from (iii) and (iv) ,

we get

1 + y + y = 5 or

2y = 4 or

y = 2..............(v)

again from (iii) and (v) ,

we get x = 1 + 2 = 3

Hence x = 3 , y = 2

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