Question

1/2x+1/3y=2 तथा1/3x+1/2y=13/6 को रैखिक समीकरण युग्म में बदल कर x और y का मान ज्ञात कीजिये
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Answer 1

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

3x + 2y 2

____________= _____

6 1

By cross multipliy

3x+2y= 12-------------(1)

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

2x + 3y 13

____________= ____

6 6

By cross multiply

12x+18y= 78-------------(2)

Multiply by 4, in eq------(1)

By cross multiplication method

12x + 8y = 48

12x + 18y = 78

- - -

______________________

0 - 10y = - 30

Minus(-) se Minus (-) cancel ❌ ho jaega.

y= 30/10

y= 3

Put the value of Y= 3, in eq-------(1)

3x+2y= 12

3x+2(3) = 12

3x+6= 12

3x= 12-6

3x= 6

x= 6/3

x= 2

The value of X= 2 and Y= 3

Answer 2

Answer:

( 1/2, 1/3 )

Step-by-step explanation:

Let  $\frac{1}{x} = a$ and $\frac{1}{y} =b$  and  xy ≠ 0 , then

$\frac{1}{2}a + \frac{1}{3}b=2$ ..... (1)

$\frac{1}{3} a+\frac{1}{2} b=\frac{13}{6}$ ..... (2)

(1) × 6 and (2) × 6

3a + 2b = 12

2a + 3b = 13

$A=\left[\begin{array}{cc}3&2&\\2&3&\\\end{array}\right] = 9-4=5$

$A_{a} \left[\begin{array}{cc}12&2&\\13&3&\\\end{array}\right] =36-26=10$

$A_{b}= \left[\begin{array}{cc}3&12&\\2&13&\\\end{array}\right] =39-24=15$

$a=\frac{A_{a} }{A} =2$

$b=\frac{A_{b} }{A} =\frac{15}{5} =3$

1/x = 2 ⇒ x = 1/2

1/y = 3 ⇒ y = 1/3

( 1/2, 1/3)