Question

If x+ay =b and ax-by=c Then find out x , y . (with process)

Answer 1

Answer:

The solution of the given system of equations is,

$x=\frac{b^2+ac}{a^2+b};\; y=\frac{ab-c}{a^2+b}$

Step-by-step explanation:

The given equations are :

x + ay = b          .......(1)

ax - by = c        .......(2)

We will use 'Substitution Method' to solve the given system of equations.

In this method, we will find out the value of either of the two variables that is 'x' and 'y' from one of the two equations in terms of the another variable  and then substitute that value in the other equation to find the value of the another variable.

Now, we will be finding out the value of 'x' in terms of 'y' from equation (1) and then substitute it in the equation (2).

Consider the equation (1), that is,

   x + ay = b ⇒ x = b - ay          ........(3)

Substitute the value of 'x' from (3) in (2), we get

  a(b - ay) - by = c

⇒ab - a²y - by = c

⇒-a²y - by = c - ab

⇒-y(a²+b) = c - ab

⇒y(a²+b) = ab - c

$\implies y=\frac{ab-c}{a^{2}+b}$

Now, substituting the above value of 'y' in equation (3), we get

$x=b-a(\frac{ab-c}{a^2+b})$

$\implies x=\frac{b(a^2+b)-a(ab-c)}{a^2+b}$

$\implies x=\frac{a^2b+b^2-a^2b+ac}{a^2+b}$

$\implies x = \frac{b^2+ac}{a^2+b}$

Hence, the solution of the given system of equations is,

$x = \frac{b^2+ac}{a^2+b} ;\; y = \frac{ab-c}{a^2+b}$