Question

Solve the following systems of equations:

x + y = 5xy
3x + 2y = 13xy

Answer 1

The given system of equation is

x + y = 5xy   ...(i)

3x + 2y = 13xy  ...(ii)

Multiplying equation (i) by 2 and equation (ii) by, we get

2x + 2y = 10xy  ...(iii)

3x + 2y = 13xy  ...(iv)

Subtracting equation (iii) from equation (iv), we get

3x – 2x = 13xy – 10xy

⇒ x = 3xy

`=> x/(3y) = y`

`=> y = 1/3`

Putting y = 1/3 in equation (i), we get

`x + y = 5 xx x xx 1/3`

`x + 1/3 = (5x)/3`

`=> 1/3  = (5x)/3 - x`

`=> 1/3 = (5x - 3x)/3`

⇒ 1 = 2x

⇒ 2x = 1

`=> x = 1/2`

Hence, solution of the given system of equations is `x = 1/2, y = 1/3`