Q. 34.7( 10 Votes )

# Solve the following system of equations by cross - multiplication method.

a(x + y) + b(x – y) = a^{2} – ab + b^{2}

a(x + y) – b(x – y) = a^{2} + ab + b^{2}

Answer :

The given system of equations can be re - written as

ax + ay + bx – by – a^{2} + ab – b^{2} = 0

⇒(a + b)x + (a – b)y – (a^{2} – ab + b^{2} ) = 0 …(1)

and ax + ay – bx + by – a^{2} – ab – b^{2} = 0

⇒ (a – b)x + (a + b)y – (a^{2} + ab + b^{2} ) = 0 …(2)

Now, by cross – multiplication method, we have

By cross - multiplication method, we have

On taking I and III ratio, we get

On taking II and III ratio, we get

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PREVIOUSSolve the following pair of equations by cross - multiplication method.ax + by = a2 – b2NEXTWhich of the following pair of linear equations has unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it by using cross - multiplication method:x – 3y – 7 = 03x – 3y – 15 = 0

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