Question

solve the following simultaneous equations​

Answer 1

EXPLANATION.

⇒ x + y = 5 xy. - - - - - (1).

⇒ 3x + 2y = 13 xy. - - - - - (2).

As we know that,

From equation (1) & (2), we get.

Multiply equation (1) by 3.

Multiply equation (2) by 1.

We get,

⇒ x + y = 5 xy. - - - - - (1) x 3.

⇒ 3x + 2y = 13 xy. - - - - - (2) x 1.

We get,

⇒ 3x + 3y = 15 xy. - - - - - (3).

⇒ 3x + 2y = 13 xy. - - - - - (4).

Subtract equation (3) & (4), we get.

⇒ y = 2 xy.

⇒ 1 = 2x.

⇒ x = 1/2.

Put the value of x = 1/2 in equation (1), we get.

⇒ x + y = 5 xy.

⇒ 1/2 + y = 5 (1/2)y.

⇒ 1/2 + y = 5y/2.

⇒ 1/2 = 5y/2 - y.

⇒ 1/2 = 5y - 2y/2.

⇒ 1/2 = 3y/2.

⇒ 1 = 3y.

⇒ y = 1/3.

Values of x = 1/2 & y = 1/3.

Answer 2

Answer:

$\huge\bf{\underline{{Answer \: - }}}$

The give system of equation is

X + y = 5xy ...(1)

3x + 2y = 13xy ...(2)

Multiplying equation (1) by 2 and equation (2) by , we get

2x + 2y = 10xy ...(3)

3x + 2y = 13xy ...(4)

Subtracting equation (3) from equation (4), we get

= 3x - 2x = 13xy - 10xy

= X = 3xy

$= \frac{x}{3x} = y$

$= y \: = \frac{1}{3}$

putting y = 1/3 in equation (1) we get

$x \: + y \: = 5 \times x \times \frac{1}{3}$

$x \: + \frac{1}{3} = \frac{5x}{3}$

$\frac{1}{3} = \frac{5x}{3} - x$

$\frac{1}{3} = \frac{5x \: - 3x}{3}$

$= 1 = 2x$

$= 2x \: = 1$

$= x \: = \frac{1}{2}$

therefore, solution of the given system of equations is x=1/2, y= 1/3.