Question

Solve for x and y:
$\frac{2}{x} + \frac{3}{y} = 2$
$\frac{1}{x} - \frac{1}{2y} = \frac{1}{3}$
x≠0 , y≠0

I'll mark brainliest!

Answer 1

Step-by-step explanation:

Given -

2/x + 3/y = 2

1/x - 1/2y = 1/3

To Find -

Value of x and y

By Elimination method :-

Now,

[ 2/x + 3/y = 2 ] × 1

[ 1/x - 1/2y = 1/3 ] × 2

» 2/x + 3/y = 2

2/x - 1/y = 2/3

(-) (+) (-)

______________

3/y + 1/y = 2 - 2/3 (By Subtracting)

» 3 + 1/y = 6 - 2/3

» 4/y = 4/3

• » y = 3

Substituting the value of y on 2/x + 3/y = 2

» 2/x + 3/3 = 2/3

» 6 + 3x/3x = 2

» 6 + 3x = 6x

» 6 = 6x - 3x

» 6 = 3x

» x = 6/3

• » x = 2

Hence,

The value of x is 2 and y is 3

Verification :-

• 2/x + 3/y = 2

» 2/2 + 3/3 = 2

» 1 + 1 = 2

» 2 = 2

LHS = RHS

And

• 1/x - 1/2y = 1/3

» 1/2 - 1/6 = 1/3

» 3 - 1/6 = 1/3

» 2/6 = 1/3

» 1/3 = 1/3

LHS = RHS

Hence,

Verified..

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$ x = 2

$\implies$ y = 3

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

• 2/x + 3/y = 2
• 1/x - 1/y = 1/3

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

• Value of x and y.

$\large\underline\mathrm{Solution}$

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

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

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

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

$\implies$ [2/x + 3/y = 2] × 1

$\implies$ [1/x - 1/y = 1/3] × 2

2/x + 3/y = 2

2/x - 1/y = 2/3

____________________

$\implies$ 4/y = 4/3

$\implies$ y = 3

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

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

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

$\implies$ 6 + 3x = 6x

$\implies$ 6 = 6x - 3x

$\implies$ 6 = 3x

$\implies$ x = 6/3

$\implies$ x = 2

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

$\large\underline\mathrm{the \: value \: of \: x \: is \: 2 \: and \: y \: is \: 3.}$

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