Question

If $\frac{3a-5z}{3b-5y}=\frac{3a+5z}{3b+5y}$, prove that $\frac{a}{b}=\frac{z}{y}$.

Answer 1

$\frac{3a-5z}{3b-5y}=\frac{3a+5z}{3b+5y}$

$\Rightarrow \frac{3a-5z}{3a+5z}=\frac{3b-5y}{3b+5y}$ [Applying alternendo] $\left(1Mark\right)$

$\Rightarrow \frac{3a-5z+3a+5z}{3a-5z-3a-5z}=\frac{3b-5y+3b+5y}{3b-5y-3b-5y}$ [Applying componendo and dividendo] $\left(1Mark\right)$

$\Rightarrow \frac{6a}{-10z}=\frac{6b}{-10y}$

$\Rightarrow \frac{a}{z}=\frac{b}{y}$

$\therefore \frac{a}{b}=\frac{z}{y}$ [Applying alternendo] $\left(1Mark\right)$