Solving the following pair of equations using elimination method, gives x = a and y = -b
$\frac{x}{a} - \frac{y}{b} = 0$
$a x + b y = a^{2} + b^{2}$

True

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False

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Solution

The correct option is B
False

Or, bx - ay = 0 … (1)
$a x + b y = a^{2} + b^{2}$ ....(2)
Multiplying equation (1) and (2) by b and a respectively, we obtain
$b^{2} x - a b y = 0$ … (3)
$a^{2} x + a b y = a^{3} + a b^{2}$ .....(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

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