Question

Solve the equations `(x-y)(x-3y)=0` and `x^2-2xy+2y^2=0`?

Answer 1

Only solution is `x=0` and `y=0`

Explanation:

We have two equations `(x-y)(x-3y)=0` and `x^2-2xy+2y^2=0`

As `(x-y)(x-3y)=0`, we have either `x=y` or `x=3y`.

Putting these values one by one in second equation, we get

(1) When `x=y`, `y^2-2y^2+2y^2=0` or `y^2=0`. Hence solution is `x=0` and `y=0`. We can denote this as `(0,0)`

(2) When `x=3y`, `9y^2-6y^2+2y^2=0` or `5y^2=0` or `y^2=0`. Hence solution is again `x=0` and `y=0`.

Thus only solution is `(0,0)`