1. ## question on intersection

Q) Find the intersection of the lines $ax+by+a^2= 0$ and $bx−ay+b^2=0$

I have attached my working out but i could not find the point of intersection

i used two different methods

2. ## Re: question on intersection

$\begin{pmatrix}a &b \\ b &-a\end{pmatrix}\begin{pmatrix}x \\ y \end{pmatrix} = \begin{pmatrix}-a^2 \\ -b^2 \end{pmatrix}$

$\begin{pmatrix}a &b &| &-a^2\\ b &-a &| &-b^2\end{pmatrix}$

$\left( \begin{array}{ccc} 1 & \frac{b}{a} & -a \\ b & -a & -b^2 \\ \end{array} \right)$

$\left( \begin{array}{ccc} 1 & \frac{b}{a} & -a \\ 0 & -\frac{b^2}{a}-a & a b-b^2 \\ \end{array} \right)$

$\left( \begin{array}{ccc} 1 & \frac{b}{a} & -a \\ 0 & 1 & \frac{a b (b-a)}{a^2+b^2} \\ \end{array} \right)$

$\left( \begin{array}{ccc} 1 & 0 & -\frac{a^3+b^3}{a^2+b^2} \\ 0 & 1 & \frac{a b (b-a)}{a^2+b^2} \\ \end{array} \right)$

$x = -\dfrac{a^3+b^3}{a^2+b^2}$

$y = \dfrac{a b (b-a)}{a^2+b^2}$