Solve the following two linear equation by substitution and elimination method: ax+by=(a-b) , bx-ay=(a-b) ?

1 Answer
Nov 12, 2017

x=(a^2-b^2)/(a^2+b^2) and y=(2ab-a^2-b^2)/(a^2+b^2)

Explanation:

a*(ax+by)+b*(bx-ay)=a*(a-b)+b*(a-b)

a^2*x+aby+b^2*x-aby=a^2-ab+ab-b^2

(a^2+b^2)*x=a^2-b^2

x=(a^2-b^2)/(a^2+b^2)

So,

a*(a^2-b^2)/(a^2+b^2)+by=a-b

a*(a^2-b^2)+by*(a^2+b^2)=(a-b)*(a^2+b^2)

a^3-ab^2+(a^2+b^2)*by=a^3+ab^2-a^2*b-b^3

(a^2+b^2)*by=2ab^2-a^2*b-b^3

y=(2ab^2-a^2*b-b^3)/[b*(a^2+b^2)]

=(2ab-a^2-b^2)/(a^2+b^2)