Question

Solve the following systems of equations.
$2y^2+xy-x^2=0,x^2-xy-y^2+3x+7y+3=0$

Answer 1

$2y^2+xy-x^2=\mathrm{0...}\left(i\right)$

$x^2-xy-y^2+3x+7y+3=0...\left(ii\right)$

Simplifying equation (i)

$2y^2+xy-x^2=0$

Or, $x^2=2y^2+xy...\left(iii\right)$

Putting this value in equation (ii)

$2y^2+xy-xy-y^2+3x+7y+3=0$

or, $y^2+7y+3x+3=0$

or, $y(y+7)+3(x+1)=0$

or, $y(y+7)=-3(x+1)$

or, $(y+7)=\frac{-3(x+1)}{y}....\left(iv\right)$

Hence, the solution of the given pair of equations

will be every pair of x & y which satisfies equation

(iv).

So, Hence will be infinite solutions.