Question

solve the following pair of linear equations- (a-b) x + (a+b) y = a^2- 2ab- b^2 & (a+b) (x+y)= a^2+b^2​

Answer 1

Answer:

(a−b)x+(a+b)y=a

2

−2ab−b

2

----- (i)

(a+b)(x+y)=a

2

+b

2

-------- (ii)

Subtracting eq (i) by eq (ii), we get.

⇒(a−b)x−(a+b)x=a

2

−2ab−b

2

−a

2

−b

2

⇒−2bx=−2bx(a+b)

⇒x=(a+b)

∴(a+b)(a+b+y)=a

2

+b

2

⇒(a+b)

2

+(a+b)y=a

2

+b

2

⇒y=

a+b

−2ab

Ans.

Answer 2

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$(a-b)x+(a+b)y=a^{2} -2ab-b^{2}$_____(i)

⇒$(a+b)(x+y)=a^{2} +b^{2}$

$(a+b)x+(a+b)y=a^{2}+ b^{2}$_________(ii)

subtracting equation ($2$) and ($1$),we obtain

$(a-b)x-(a+b)x=(a^{2} -2ab-b^{2} )$

$(a-b-a-b)x=-2ab-2b^{2}$

$-2bx=-2b(a+b)$

$x=a+b$

Using Equation (i),we obtain

$(a-b)(a+b)+(a+b)=a^{2}- 2ab-b^{2}$

$a^{2} -b^{2} +(a+b)y=a^{2} -2ab-b^{2}$

$(a+b)y=-2ab$

$y=\frac{2ab}{(a+b)}$

$\huge\mathcal\colorbox{black}{{\color{red}{Hope\:It\:Helps}}}$