Question

solve for X and y 99x+101y=499:101x+99y=501

Answer 1

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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Answer 2

Hello !!

99X + 101Y = 499 -----------(1)

And,

101X + 99Y = 501 -------------(2)

From equation (1) we get,

99X + 101Y = 499

99X = ( 499 - 101Y )

X = ( 499 - 101Y)/99 -----------(3)

Putting the value of X in equation (2)

101X + 99Y = 501

101 × ( 499 - 101Y)/99 + 99Y = 501

50399 - 10201Y/99 + 99Y = 501

50399 - 10201Y + 9801Y = 501 × 99

9801Y - 10201Y = 49599 - 50399

-400Y = -800

Y = 800/400

Y = 2

Putting the value of Y in equation (3)

X = ( 499 - 101Y)/99 = ( 499 - 101 × 2 ) /99

X = (499 - 202)/99 = 207/99

X = 3

Hence,

X = 3 and Y = 2.