Question

Guys Pls help me with the sum in the attachment ASAP​

Answer 1

Solution

Given :-

• ax + by = a -------equ(1)
• -bx + ay = b -------equ(2)

Find :-

• Value of x & y

Explanation

Multiply by " b " in equ(1) & " a " in equ(2)

• ab x + b² y = ab

And,

• -ab x + a² y = ab

_________________add. it's

==> (b²+a²)y = 2ab

==> y = 2ab/(b²+a²)

keep value of y in equ(1)

==> ax + b * [2ab/(b²+a²)] = a

==> ax = a - 2ab²/(b²+a²)

==> ax = (ab²+a³-2ab²)/(b²+a²

==> ax = a(a²-b²)/(b²+a²)

==> x = (-b²+a²)/(b²-a²)

Thus

• Value of x = (-b²+a²)/(b²+a²)
• Value of y = 2ab/(b²+a²)

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Verification

Keep value of x & y in equ(1)

==> a * (-b²+a²)/(b²+a²) + b* 2ab/(b²+a²) = a

==> 1/(a²+b²)[ -ab²+a³+2ab² ] = a

==> 1/(a²+b²)[a³+ab²] = a

==> a[ (a²+b²)/(a²+b²)] = a

==> a = a

L.H.S. = R.H.S.

That's proved.

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