Question

) If Solve the following pair of linear equation
99x + 101y = 499xy
101x + 99y = 501xy

Answer 1

given equation :-

$\tt \: 99x + 101y = 499xy.......eq.(1) \\ \tt101x + 99y = 501xy.......eq.(2)$

Solution :-

add eq.(1) and (2) we get ----

$\tt \: 99x + 101y = 499xy \\ \tt101x + 99y = 501xy \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \tt \: 200x + 200y = 1000xy \\ \\ \sf \: divided \: of \: 200xy \: in \: both \: side \: we \: get\: \\ \\ \bf \: x + y =5xy\: ............eq.(3)$

Now,

Subtract eq. (1) from eq.(2) ---

$\tt \: 101x + 99y = 501xy \\ \tt \: 99x + 101y = 499 xy\\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \tt \: 2x - 2y = 2xy \\ \sf \: divided \: by \: 2 \: in \: both \: side \: we \: get \: \\ \bf \: x - y = 1 \: .............eq.(4) \\ \\ \sf \: sign \: will \: be \: change \: as \: 99x \:will \: \\ \sf convert \: \sf \: into \: ( - 99x) \: and \: 101y \: \\ \sf \: will \: convert \: into \: ( - 101y)$

NOW,

add eq.(3) and eq.(4) we get --

$\tt \: x + y = 5xy \\ \tt \: x - y = 1xy \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \tt \: 2x = 6xy \\ \therefore \tt \: \: y = \dfrac{2x}{6x} = \bf \: \dfrac{1}{3}\\ \\ \bf \: put \: value \: of \: y = \dfrac{1}{3}\: in \: eq.(4) \: we \: get \: \\ \\ \tt x - \dfrac{1}{3}= x \times\dfrac{1}{3}\\ \\ \tt \: \: \dfrac{3x-3}{3}= \dfrac{x}{3}\\ \\ \tt \:9x-3= 3x \\ \\ \tt \:9x-3x = 3\\ \\ \tt \: 6x=3 \\ \\ \tt \: {x = \dfrac{3}{6}}\\ \\ \bf \: {x = \dfrac{1}{2}}$

therefore the value of x = $\tt\: \dfrac{1}{2}$ and y = $\tt\: \dfrac{1}{3}$

Answer 2

Answer:

The Values are x=1\2 and y=1/3

Step-by-step explanation:

99x+101y=499xy---------------------1

101x+99y=501xy---------------------2

Add 1 and 2

1= 99x+101y=499xy

2=101x+99y=501xy

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200x+200y=1000xy

Divide by 200

x+y=5----------------------3

Sub 1 and 2

2=101x+99y=501xy

1= 99x+101y=499xy(-)

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2x-2y=2xy

Divide by 2

x-y=1xy-----------4

after do it yourself after do it yourselffffff