Question

99x + 101y = 499 101x + 99y = 501 solve above equation and find value of x and y​

Answer 1

Step-by-step explanation:

first add both the equation 1 and 2 given in the question

99x + 101y= 499

101x+ 99y =501

200x+200y=1000( by adding)

200(x+y)=1000

x+y= 5(say it equation 1)

now subtract both the equation 1 and 2 given in the question

99x +101y =499

101x+ 99y =501

(-) (-) (-)

-2x+2y=-2

-2(x-y)=-2

x-y=1 (say it equation 2)

now add equation 1 and 2 which are numbered

x+y=5

x-y=1

x=6

now put x in any equation 1 and 2

x+y=5

6+y=5

y=-1

Answer 2

Answer

$\sf \dashrightarrow 99x + 101y = 499 \: \: --- (i)$

$\sf \dashrightarrow 101x + 99y = 501 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 99x = 499 - 101y$

$\sf \dashrightarrow x = \dfrac{499 - 101y}{99}$

Now, let's find the value of y by second equation.

$\sf \dashrightarrow 101x + 99y = 501$

$\sf \dashrightarrow 101 \bigg( \dfrac{499 - 101y}{99} \bigg) + 99y = 501$

$\sf \dashrightarrow \dfrac{50399 - 10201y}{99} + 99y = 501$

$\sf \dashrightarrow \dfrac{50399 - 10201y + 9801y}{99} = 501$

$\sf \dashrightarrow \dfrac{50399 - 400y}{99} = 501$

$\sf \dashrightarrow 50399 - 400y = 501 \times 99$

$\sf \dashrightarrow 50399 - 400y = 49599$

$\sf \dashrightarrow -400y = 49599 - 50399$

$\sf \dashrightarrow -400y = -800$

$\sf \dashrightarrow y = \dfrac{-800}{-400}$

$\sf \dashrightarrow y = 2$

Now, let's find the value of x by first equation.

$\sf \dashrightarrow 99x + 101y = 499$

$\sf \dashrightarrow 99x + 101(2) = 499$

$\sf \dashrightarrow 99x + 202 = 499$

$\sf \dashrightarrow 99x = 499 - 202$

$\sf \dashrightarrow 99x = 297$

$\sf \dashrightarrow x = \dfrac{297}{99}$

$\sf \dashrightarrow x = 3$

Hence, the values of x and y are 2 and 3.