Question

Solve the following systems of equations:
1/(3x + y) + 1/(3x – y) = 3/4
1/ 2(3x + y) – 1/ 2(3x – y) = -(1/8)

Answer 1

x = y = 0

or

x = y = 1

Solving system of equations :-

1. We will first use cross-multiplication method to reduce the given equations in their simplest forms.
2. After solving the process of cross-multiplication, we will get two equations which we will further solve by elimination process.
3. By elimination process, we will get the value of x = y which we will substitute in the reduced equations we got and by that we will get the real values for x and y.

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Answer 2

The value of x and y for system of equation is 0 ,0 and 1 , 1  

Step-by-step explanation:

Given as :

The system of equation are

$\dfrac{1}{3x+y}$ + $\dfrac{1}{3x-y}$   = $\dfrac{3}{4}$                  

$\dfrac{1}{2(3x+y)}$ - $\dfrac{1}{2(3x-y)}$ = $\dfrac{-1}{8}$

solving the system of equation by

Taking LCM

$\dfrac{(3x-y)+(3x+y)}{(3x+y)(3x-y)}$ = $\dfrac{3}{4}$

Or, $\dfrac{6x}{(3x+y)(3x-y)}$ = $\dfrac{3}{4}$

By cross multiplication

Or, 4 (6 x) = 3 (9 x² - y² )

Or, 8 x = 9 x² - y²

∴  9 x² - y² - 8 x = 0                           .......1

Again

$\dfrac{1}{2(3x+y)}$ - $\dfrac{1}{2(3x-y)}$ = $\dfrac{-1}{8}$

solving the system of equation by

Taking LCM

$\dfrac{2(3x-y)-2(3x+y)}{4(3x+y)(3x-y)}$ = $\dfrac{-1}{8}$

Or, $\dfrac{6x-2y-6x-2y}{4(3x+y)(3x-y)}$ = $\dfrac{-1}{8}$

Or, $\dfrac{-4y}{4(3x+y)(3x-y)}$ = $\dfrac{-1}{8}$

By cross multiplication

8 y = (9 x² - y² )

Or, 9 x² - y² - 8 y = 0                          ........2

Now, Solving eq 1 and eq 2

( 9 x² - y² - 8 x ) - ( 9 x² - y² - 8 y ) = 0

Or, (  9 x² -  9 x² ) + (  y² -   y² ) = 8 x - 8 y

Or, 0 + 0 = 8 x - 8 y

∴   8 x - 8 y = 0

i.e  8 x = 8 y

Or,  x = y

Now, Put the value of x = y into eq 2

i.e 9 x² - x² - 8 x = 0

Or,  8 x² - 8 x = 0

Or,  x² -  x = 0

Or, x ( x - 1 ) = 0

∴   x = 0 ,   x = 1

Similarly

y = x = 0

And y = x = 1

So, The value of x and y for system of equation = 0 ,0 and 1 , 1

Hence, The value of x and y for system of equation is 0 ,0 and 1 , 1  Answer