Book Online Demo

Check Your IQ

Try Test

Courses

Solve the following system of equations using substitution method: $ax - by = 0, a b^{2} x + a^{2} by - (a^{2} + b^{2}) = 0$

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

x = \frac{1}{a}

and

y = \frac{1}{b}

x = \frac{1}{9 a}

and

y = \frac{4}{b}

x = \frac{2}{a}

and

y = \frac{a}{b}

x = \frac{b}{a}

and

y = \frac{a^{2}}{b}

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given equation is,

ax - by = 0

It can be written as

ax = by

x = \frac{b}{a} y

….(1)
Another equation given in the problem,

a b^{2} x + a^{2} by = a^{2} + b^{2}

Put value of x in this equation,

a b^{2} x + a^{2} by = a^{2} + b^{2}

a b^{2} \times \frac{b}{a} y + a^{2} by = a^{2} + b^{2}

b^{3} y + a^{2} by = a^{2} + b^{2}

y (b^{3} + a^{2} b) = a^{2} + b^{2}

y = \frac{a^{2} + b^{2}}{b^{3} + a^{2} b} = \frac{a^{2} + b^{2}}{b (a^{2} + b^{2})}

y = \frac{1}{b}

Put this value in equation 1,

x = \frac{b}{a} \times \frac{1}{b}

x = \frac{1}{a}

Thus,

x = \frac{1}{a}

and

y = \frac{1}{b}

Correct option is 1.

Watch 3-min video & get full concept clarity