Question

solve the following simultaneous equations​

Answer 1

EXPLANATION.

⇒ 2u + 15v = 17 uv. - - - - - (1).

⇒ 5u + 5v = 16 uv. - - - - - (2).

As we know that,

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

Multiply equation (1) by 5.

Multiply equation (2) by 2.

We get,

⇒ 2u + 15v = 17 uv. - - - - - (1) x 5.

⇒ 5u + 5v = 16 uv. - - - - - (2) x 2.

We get,

⇒ 10u + 75v = 85 uv. - - - - - (3).

⇒ 10u + 10v = 32 uv. - - - - - (4).

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

⇒ 65v = 53 uv.

⇒ 65 = 53 u.

⇒ u = 65/53.

Put the value of u = 65/53 in equation (1), we get.

⇒ 2u + 15v = 17 uv.

⇒ 2(65/53) + 15v = 17(65/53)v.

⇒ 130/53 + 15v = (1105/53)v.

⇒ 130/53 = 1105/53v - 15v.

⇒ 130/53 = v(1105/53 - 15).

⇒ 130/53 = v(1105 - 795/53).

⇒ 130/53 = v(310/53).

⇒ 130 = 310v.

⇒ v = 13/31.

Value of u = 65/53 & v = 13/31.

Answer 2

Answer:

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

2u + 15v = 17uv , 5u + 5v = 16uv

2u + 15v = 17uv Multiply with 5 on both sides

10u + 75v = 85uv ....(1)

5u + 5v = 16uv Multiply with 2 on both sides

10u + 10v = 32uv ...(2)

10u + 75v = 85uv

- 10u + 10v = 32uv

_______________

0 + 65v = 53uv

$u \: = \frac{65}{53}$

substitute in equation

$10( \frac{65}{53}) + 10v = 32 (\frac{65}{53})v$

$\frac{650}{53} = v \: (\frac{2080}{53} - 10)$

$\frac{650}{53} = v \: ( \frac{1550}{53})$

$v \: = \frac{13}{31}$