Question

Question 7 (iv)
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

$(a-b)x+(a+b)y=a^2-2ab-b^2$ ....(1)
$(a+b)(x+y)=a^2+b^2$
$(a+b)x+(a+b)y=a^2+b^2$ .....(2)
Subtracting equation (2) from (1), we obtain
$(a-b)x-(a+b)x=(a^2-2ab-b^2)-(a^2+b^2)$
$(a-b-a-b)x=-2ab-2b^2$
$-2bx=-2b(a+b)$
$x=a+b$
Using equation (1), we obtain
$(a-b)(a+b)+(a+b)y=a^2-2ab-b^2$
$a^2-b^2+(a+b)y=a^2-2ab-b^2$
$(a+b)y=-2ab$
$y=\frac{-2ab}{a+b}$