Question

2y - 3x = 15xy ; 8y + 5x = 77xy
(divide both equation in xy)
pls help me ​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Finally, we get x = 1/9 and y = 1.

Given,

2y - 3x = 15xy

8y + 5x = 77xy

To Find,

Solution for the system of equations

Solution,

We have been given a system of equations in two variables

2y - 3x = 15xy           (1)

8y + 5x = 77xy          (2)

Let us divide both the equations by 'xy'

Dividing (1) by 'xy'

$\frac{2y}{xy} - \frac{3x}{xy} = \frac{15xy}{xy}$

$\frac{2}{x} - \frac{3}{y} = 15$

Dividing (2) by 'xy'

$\frac{8y}{xy} + \frac{5x}{xy} = \frac{77xy}{xy}$

$\frac{8}{x} + \frac{5}{y} = 77$

Now let us take 1/x = a and 1/y = b

Framing new equations we get,

2a - 3b = 15         (3)

2a = 15 + 3b

8a + 5b = 77        (4)

4(2a) + 5b = 77

Substituting the value of 2a in (4)

4(15 + 3b) + 5b = 77

60 + 12b + 5b = 77

17b = 77 - 60

17b = 17

b = 1

Further,

2a = 15 + 3(1)

2a = 15 + 3

2a = 18

a = 9

Hence we get,

a = 1/x = 9

x = 1/9

b = 1/y = 1

y = 1

Thus, finally x = 1/9 and y = 1.

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