Question

3/x+y + 2/x-y = 2 And 9/x+y - 4/x-y = 1
Solve For X And Y By Elimination Method​

Answer 1

Answer:

$x = \frac{5}{2}$

$y =\frac{1}{2}$

Step-by-step explanation:

Given :

To find the value of x & y if,

$\frac{3}{x+y} + \frac{2}{x-y} = 2$  ..(i)

&

$\frac{9}{x+y} - \frac{4}{x-y} = 1$  ..(ii)

Solution :

Adding both the equations,.

⇒ (i) × 2 + (ii)

⇒ $(\frac{3}{x+y} + \frac{2}{x-y})(2) + (\frac{9}{x+y} - \frac{4}{x-y}) = 2(2) + 1$

⇒ $\frac{6}{x+y} + \frac{4}{x-y} + (\frac{9}{x+y} - \frac{4}{x-y}) = 5$

⇒ $\frac{15}{x+y} = 5$

⇒ $\frac{x + y}{15} =\frac{1}{5}$

⇒ $x + y =\frac{15}{5}$

⇒ $x + y =3$ ..(iii)

By substituting value of (iii) in (i),

We get,

⇒ $\frac{3}{x+y} + \frac{2}{x-y} = 2$

⇒ $\frac{3}{3} + \frac{2}{x-y} = 2$

⇒ $1 + \frac{2}{x-y} = 2$

⇒ $\frac{2}{x-y} = 2 - 1$

⇒ $\frac{2}{x-y} = 1$

⇒ $x-y = 2$ ...(iv)

By adding (iii) & (iv),

We get,

⇒ (iii) + (iv) ⇒ $(x + y) + (x - y) = 3 + 2$

⇒ $2x= 5$

⇒ $x = \frac{5}{2}$

By subtracting (iv) from (iii),

We get,

⇒ (iii) - (iv) ⇒ $(x + y) - (x - y) = 3 - 2$

⇒ $2y = 1$

⇒ $y =\frac{1}{2}$

∴ $x = \frac{5}{2}$

∴ $y =\frac{1}{2}$

Answer 2

Answer:

Value of x is 5/2 and y is 1/2

Step-by-step explanation:

Let 1/x+y = a and 1/x-y = b

3a+2b=2 ......(i)

9a-4b=1.......(ii)

On multiplying (i) by 3 and (ii) by 1 and subtracting, we get,

27a+18b=18

27a-12b=3

(-). (+). (-)

We get b= 1/2 and a= 1/3

Now 1/x+y = 1/3

so, x+y = 3 .....(iii)

and 1/x-y = 1/2

so, x-y= 2.....(iv)

We are adding equation (iii) and (iv),

x+y+x-y = 3+2

so,x= 5/2

Again we are subtracting equation (ii) from Equation (i),

x+y-x+y= 3-2

So,y= 1/2