Question

(a+b)x+(a-b)y=a²+b² ; (a-b)x+(a+b)y=a²+b² solve by substitution method

Answer 1

Answer:

(a+b)x+(a-b)y=a²+b²----(I)

(a-b){(a+b)x+(a-b)y}=(a²+b²)(a-b)

(a²-b²)x+(a-b)²y=(a²+b²)(a-b) ------ (II)

Step-by-step explanation:

(a-b)x+(a+b)y=a²+b²----(III)

(a+b){(a-b)x+(a+b)y}=(a²+b²)(a+b)

(a²-b²)x+(a+b)²y=(a²+b²)(a+b) ------(IV)

So, (II) - (IV)

(a²-b²)x+(a-b)²y-(a²-b²)x-(a+b)²y=(a-b)(a²+b²)-(a+b)(a²+b²)

-(a+b)²y+(a-b)²y=(a²+b²){a-b-a-b}

-y{(a+b)²-(a-b)²}=-2b(a²+b²)

y.4ab=2b(a²+b²)

y=a²+b²/2a

So, get from number -(I) equation

(a+b)x+(a-b)(a²+b²)/2a=a²+b²

(a-b)x=a²+b²-(a-b)(a²+b²)/2a

(a-b)x={2a(a²+b²)-(a-b)(a²+b²)}/2a

(a-b)x=(a²+b²)(2a-a+b)/2a

(a-b)x=(a²+b²)(a+b)/2a

x=(a²+b²)/2a

So, x=(a²+b²)/2a and, y=(a²+b²)/2a