Question

$ax + by = 2ab \: \: \: \: \: \: \: \: \: \: \: \: bx + ay = {a }^{2} + {b}^{2}$
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Answer 1

Step-by-step explanation:

$ax + by = 2ab$

and

$bx + ay = {a}^{2} + {b}^{2}$

On solving both,

Refer the image above.

Thank you

Answer 2

Answer:

x = b

y = a

Solution:

The given equations are :

ax + by = 2ab --------(1)

bx + ay = a² + b² ---------(2)

Now,

Multiplying both sides of the eq-(1) by a ,

We get ;

=> a•(ax + by) = a•(2ab)

=> a²x + aby = 2a²b ---------(3)

Also,

Multiplying both sides of the eq-(2) by b ,

We get ;

=> bx + ay = a² + b²

=> b•(bx + ay) = b•(a² + b²)

=> b²x + aby = a²b + b³ -------(4)

Now,

Subtracting eq-(4) from eq-(3) ,

We have ;

=> (a²x+aby) - (b²x+aby) = 2a²b - (a²b + b³)

=> a²x + aby - b²x - aby = 2a²b - a²b - b³

=> a²x - b²x = a²b - b³

=> x(a² - b²) = b(a² - b²)

=> x = b(a² - b²)/(a² - b²)

=> x = b

Now,

Putting x = b in eq-(1) , we get ;

=> ax + by = 2ab

=> ab + by = 2ab { ° . ° x = b }

=> by = 2ab - ab

=> by = ab

=> y = ab/b

=> y = a

Hence,

x = b and y = a