Question

Question 7 (iii)
Solve the following pair of linear equations.
$\frac{x}{a}-\frac{y}{b}=0$
$ax+by=a^2+b^2$

Answer 1

Or, bx - ay = 0 … (1)
$ax+by=a^2+b^2$ ....(2)
Multiplying equation (1) and (2) by b and a respectively, we obtain
$b^{2}x-aby=0$ … (3)
$a^{2}x+aby=a^3+a{b}^2$ .....(4)
Adding equations (3) and (4), we obtain
$b^{2}x+a^{2}x=a^3+a{b}^3$
$x(b^2+a^2)=a(a^2+b^2)$
x=a
By using (1), we obtain
b (a) - ay = 0
ab - ay = 0
ay = ab
y = b