Solve the following pair of linear equations:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$

(A) Given equations are:
$\frac{x}{a} - \frac{y}{b} = 0 \implies bx - ay = 0 \quad \dots(1)$
$ax + by = a^2 + b^2 \quad \dots(2)$
To solve by elimination,multiply equation $(1)$ by $b$ and equation $(2)$ by $a$:
$b^2x - aby = 0 \quad \dots(3)$
$a^2x + aby = a(a^2 + b^2) = a^3 + ab^2 \quad \dots(4)$
Adding equations $(3)$ and $(4)$:
$(b^2x - aby) + (a^2x + aby) = 0 + a^3 + ab^2$
$x(a^2 + b^2) = a(a^2 + b^2)$
$x = a$
Substitute $x = a$ into equation $(1)$:
$b(a) - ay = 0$
$ab - ay = 0$
$ay = ab$
$y = b$
Thus,the solution is $x = a$ and $y = b$.