Question

X+y = a+b and ax-by = a² - b²
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Answer 1

Given : Equations $x+y=a+bx+y=a+b \: and \: ax-by=a^2-b^2ax−by=a$

To find : Solve the equations ?

Solution :

$Let \: x+y=a+bx+y=a+b \implies(1) \\ ax-by=a^2-b^2ax−by=a \implies(2)$

Substitute x from (1) in equation (2),

$a(a+b-y)-by=a^2-b^2a(a+b) \\a^2+ab-ay-by=a^2-b^2a \\ab-ay-by=-b^2ab−ay−by=−b² ab-y(a+b)\\=-b^2ab−y(a+b) \\ =−b²</p><p>y(a+b)=ab+b^2y(a+b)=ab+b² \\y(a+b)=b(a+b)y(a+b)=b(a+b) \\ y=by=b$

Substitute y in equation (1),

$x+b=a+bx+b=a+b \\x=a+b-bx=a+b−b \\ x=ax=a$

Therefore, The solution of the equations is x=a and y=b.