Question

solve by reducing them to a pair of linear equations


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Answer 1

Step-by-step explanation:

Given -

1/2x + 1/3y = 2

1/3x + 1/2y = 13/6

To Find -

• Value of x and y

Now,

1/2x + 1/3y = 2

→ 3y + 2x/6xy = 2

→ 3y + 2x = 12xy ...... (i)

And

1/3x + 1/2y = 13/6

→ 2y + 3x/6xy = 13/6

→ 2y + 3x = 13xy ........ (ii)

Now, From (i) and (ii), we get :

[ 3y + 2x = 12xy ] × 2

[ 2y + 3x = 13xy ] × 3

→ 6y + 4x = 24xy

6y + 9x = 39xy

(-) (-) (-)

______________

-5x = -15xy

→ y = 1/3

Now,

Substituting the value of y on (i), we get :

3y + 2x = 12xy

→ 3×1/3 + 2x = 12x × 1/3

→ 1 + 2x = 4x

→ 2x = 1

→ x = 1/2

Hence,

The value of x is 1/2 and y is 1/3

Answer 2

$\huge \mathfrak{Answer:-}$

$\large\underline\mathrm{The \: value \: of \: x \: is \: 1/2 \: and \: y \: is \: 1/2.}$

$\large\underline\mathrm{Given:-}$

• (1/2)x + (1/3)y = 2
• (1/3)x + (1/2)y = 13/6

$\large\underline\mathrm{To \: find}$

• Value of x and y

$\large\underline\mathrm{Solution}$

$\implies$ (1/2)x + (1/3)y = 2

$\implies$ 3y + 2x/6xy = 2

$\implies$ 3y + 2x = 12xy. ..(1)

$\large\underline\mathrm{and}$

$\implies$ (1/3)x + (1/2)y = 13/6

$\implies$ 2y + 3x/6xy = 13/6

$\implies$ 2y + 3x = 13xy. ..(2)

$\large\underline\mathrm{Now,}$

$\large\underline\mathrm{Eq. \: (1) \: × \: 2 \: and \: Eq. \: (2) \: × \: 3. we \: get.}$

$\implies$ [3y + 2x = 12xy] × 2

$\implies$ [2y + 3x = 13xy] × 3

$\implies$ 6y + 4x = 24xy

$\implies$ 6y + 9x = 39xy

$\implies$ -5x = -15xy

$\implies$ y = 1/3

$\large\underline\mathrm{now,}$

$\large\underline\mathrm{putting \: the \: value \: of \: y \: on \: Eq. \: (1)}$

$\implies$ 3y + 2x = 12xy

$\implies$ 3 × 1/3 + 2x = 12xy

$\implies$ 1 + 2x = 4x

$\implies$ 2x = 1

$\implies$ x = 1/2

$\large\underline\mathrm{hence, }$

$\large\underline\mathrm{The \: value \: of \: x \: is \: 1/2 \: and \: y \: is \: 1/2.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$