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Question
Solve the following pair of linear equations.
`x/a-y/b = 0`
ax + by = a2 + b2
Solution
`x/a-y/b = 0`
Or, bx − ay = 0 … (1)
ax + by = a2 + b2 … (2)
Multiplying equation (1) and (2) by b and a respectively, we obtain
b2x − aby = 0 … (3)
a2x + aby = a3 + ab2 … (4)
Adding equations (3) and (4), we obtain
b2x + a2x = a3 + ab2
x (b2 + a2) = a (a2 + b2)
x = a
By using (1), we obtain
b (a) − ay = 0
ab − ay = 0
ay = ab
y = b
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