Question

x/a + y/b= 0
(a+b)x + (a-b)y= a^2+b^2

Solve the following pair of equation by cross multiplication method

Answer 1

x/a+y/b=0
=>bx+ay=0
=>x=-ay/b------------------(1)
(a+b)x+(a-b)y=a²+ b²
=>(a+b)x=a²+ b²+by-ay
=>x=(a²+b²+by-ay)/(a+b)
=>-ay/b=(a²+b²+by-ay)/(a+b)
=>(a+b)(-a/b)y=a²+b²+y(b-a)
=>y{(-a²-ab)/b -b +a}=a²+b²
=>y=(a²+b²)/{(-a²-b²)/b}
=>y=-b
so, from Equation 1, x=-a×-b/b
=>x=a
Solution, (x,y)=(a,-b)