Question

please ans this question by using elimination method please ans my question in step wise other wise i will report​

Answer 1

Let a = 1/x      &      b = 1/y

The Equation Now becomes: -

$\frac{a}{2}+\frac{b}{3} = 2 \\\\ \frac{a}{3}+\frac{b}{2} = \frac{13}{6}$

Equation 1

$\frac{3a + 2b}{6} =2\\\\ 3a + 2b = 12$

Multiplying above equation by 2

⇒ 6a + 4b = 24     ---------(1)

Equation 2

$\frac{2a+3b}{6} = \frac{13}{6} \\\\2a + 3b = 13$

Multiplying above equation by 3

⇒ 6a + 9b = 39   --------(2)

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Now Subtracting eq. 2 from eq. 1

We get :-

⇒ -5b = -15

⇒ b = 3

Putting value of b in eq. 1

⇒ 6a + 12 = 24

⇒ 6a = 24 - 12

⇒ 6a = 12

⇒ a = 2

${\boxed{a = 2 & b = 3}}$

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We let a = 1/x

∴ 1/x = 2

⇒ x = 1/2

We let b = 1/y

∴ 1/y = 3

⇒ y = 1/3

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${\huge{\bold{\boxed{Ans.\: x = \frac{1}{2} \:and\: y = \frac{1}{3}}}}}$

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I Hope This Will Help You