Question

(m+n)x+(m-n)y=m²-2mn-n² and (m+n)(x+y)=m²+n².Find the value of x and y.​

Answer 1

m(x+y)+n(x-y)-(m²+mn+n²)=0

n(x+y)+m(x-y)-(m²-mn+n²)=0

m(x+y)+n(x-y)-(m²+mn+n²)=0

=> (m + n)x  + (m - n)y  = m²+mn+n²    Eq1

n(x+y)+m(x-y)-(m²-mn+n²)=0

=> (m + n)x  - (m - n)y  = m²-mn+n²    Eq2

Adding both Eq1 + Eq2

=>  2(m+n)x  =  2(m² + n²)

=> x = (m² + n²)/(m + n)

Eq1 - Eq2

=> 2y(m - n)  = 2mn

=> y = mn/(m - n)

x = (m² + n²)/(m + n)

y = mn/(m - n)