Question

$50 \: points$


solve and find the value of x and y


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Answer 1

Step-by-step explanation:

ax+by=1................(i)

bx+ay=2ab/a² + b² .......................(ii)

ax+by=1    .................. *a

a²x + aby = a ....................(iii)

bx+ay=2ab/(a² + b²).......................* b

b ² x +aby = 2ab² /(a² + b²)..........(iv)

subtracting eq (iv) from (iii)

a²x + aby = a - [b ² x +aby = 2ab² /(a² + b²)]

a²x - b²x + aby - aby  = a -2ab² /(a² + b²)

(a² - b²)x = [a(a² + b²) - 2ab²]/(a² + b²)

(a² - b²)x = [a³ + ab² - 2ab²]/(a² + b²)

(a² - b²)x = [a³ - ab²]/(a² + b²)

x = [a(a² - b²)] / (a² + b²)(a² - b²)

x = a/ (a² + b²)

putting x in (i)

ax+by=1

a [a/ (a² + b²)] +by = 1

a²/(a² + b²) + by = 1

by = 1 - a²/(a² + b²)

by = [a² + b² - a²]/a² + b²

by = b²/a² + b²

y = b²/(a² + b²)(b)

y = b/a² + b²

x  = a/ (a² + b²)

y = b/a² + b²

$\huge \sf \red{hope \: it \: helps}$

Answer 2

Step-by-step explanation:

ax+by=1................(i)

bx+ay=2ab/a² + b² .......................(ii)

ax+by=1    .................. *a

a²x + aby = a ....................(iii)

bx+ay=2ab/(a² + b²).......................* b

b ² x +aby = 2ab² /(a² + b²)..........(iv)

subtracting eq (iv) from (iii)

a²x + aby = a - [b ² x +aby = 2ab² /(a² + b²)]

a²x - b²x + aby - aby  = a -2ab² /(a² + b²)

(a² - b²)x = [a(a² + b²) - 2ab²]/(a² + b²)

(a² - b²)x = [a³ + ab² - 2ab²]/(a² + b²)

(a² - b²)x = [a³ - ab²]/(a² + b²)

x = [a(a² - b²)] / (a² + b²)(a² - b²)

x = a/ (a² + b²)

putting x in (i)

ax+by=1

a [a/ (a² + b²)] +by = 1

a²/(a² + b²) + by = 1

by = 1 - a²/(a² + b²)

by = [a² + b² - a²]/a² + b²

by = b²/a² + b²

y = b²/(a² + b²)(b)

y = b/a² + b²

x  = a/ (a² + b²)

y = b/a² + b²

$\huge \sf \red{hope \: it \: helps}$