Question

if 1/x+2/y =5,3/x-1/y=8 then the value of x,y ?​

Answer 1

Step-by-step explanation:

Given,

2

x+y−8

=

3

x+2y−14

=

4

3x−y

By taking first two. we get,

2

x+y−8

=

3

x+2y−14

⇒3x+3y−24=2x+4y−28

⇒x−y=−4 .(i)

By taking last two. we get,

3

x+2y−14

=

4

3x−y

⇒4x+8y−56=9x−3y

⇒5x−11y=−56 (ii)

On multiplying equation (i) by 5. we get,

5x−5y=−20 .(iii)

On subtracting (ii) from (iii). we get,

5x−5y−(5x−11y)=−20−(−56)

∴6y=36

∴y=6

Substitute y=6 in (i). we get,

x−6=−4

∴x=2

∴x=2,y=6.

Answer 2

Concept

The alternative method can be defined as a means of algebraically solving a linear system. The substitution method works by replacing one y value with another. Simply put, the method is to find the value of variable x for variable y.

Given

We have given two equations which are  $\frac{1}{x}+\frac{2}{y} =5$ and $\frac{3}{x} -\frac{1}{y} =8$ .

Find

We are asked to determine the values of x and y in the given equations.

Solution

First of all, we will assume  $\frac{1}{x} =a$ and  $\frac{1}{y} =b$ .

Now, the equations becomes

       $a+2b=5$    ....(1)

       $3a-b=8$    ....(2)

Now, we will apply the substitution method , from equation (1) we get

     $a=5-2b$     ...(3)

We will put the value of 'a 'in equation (2) , we get

 $3(5-2b)-b=8\\15-6b-b=8\\15-8=6b+b\\7=7b\\b=1$

Putting the value of 'b' in equation (3)

 $a=5-2(1)\\=5-2\\=3$

On solving, $a=\frac{1}{x}$  we get value of x,

       $x=\frac{1}{a} \\\\x=\frac{1}{3}$    

On solving  $b=\frac{1}{y}$ we get value of y,

  $y=\frac{1}{b} \\\\y=1$

Hence, values of x and y in the given equations are $\frac{1}{3}$ and $1$ respectively.

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