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Question

Solve the following pair of equations:

xa−yb=0, ax+by=a2+b2Open in App

Solution

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The equation xa−yb=0 can be rewritten as:

bx−ay=0...........(1)

The other equation given is:

ax+by=a2+b2..........(2)

We pick either of the equations and write one variable in terms of the other.

Let us consider the equation bx−ay=0 and write it as

x=ayb

Substitute the value of x in equation ax+by=a2+b2. We get

a(ayb)+by=a2+b2⇒a2yb+by=a2+b2⇒a2y+b2yb=a2+b2⇒(a2+b2)y=b(a2+b2)⇒y=b

Therefore, y=b

Substituting this value of y in the equation x=ayb, we get

x=abb=a

Hence, the solution is x=a,y=b.

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