Question

Find the points of intersection of the following pairs of lines:
$bx+ay=ab$ and $ax+by=ab$

Answer 1

$bx+ay=ab.....\left(1\right)$

$ax+by=ab.....\left(2\right)$

From equation $\left(1\right)\&\left(2\right)$, we have

$bx+ay=ax+by$

$\Rightarrow x(b-a)=y(b-a)$

$\Rightarrow x=y$

Therefore, from equation $\left(1\right)$, we have

$bx+ax=ab$

$\Rightarrow x=\frac{ab}{a+b}$

$\therefore y=x=\frac{ab}{a+b}$

Thus the point of intersection of the given lines is $(\frac{ab}{a+b},\frac{ab}{a+b})$.