Question

solve
$\frac{x + y}{xy } = \frac{5 }{2} and \frac{x - y}{xy} = \frac{1}{2}$
​

Answer 1

Hope it helped u
Pls mark brilliant

Answer 2

Answer :-

x = 1 , y = 2/3

Explanation :-

Pair of linear equations

$\\ \\ \dfrac{x + y}{xy} = \dfrac{5}{2} \rightarrow eq(1) \\ \\ \\ \dfrac{x - y}{xy} = \dfrac{1}{2} \rightarrow eq(2)$

Simplifying eq(1)

$\\ \implies \dfrac{x + y}{xy} = \dfrac{5}{2} \\ \\ \\ \implies \dfrac{x}{xy} + \dfrac{y}{xy} = \dfrac{5}{2} \\ \\ \\ \implies \dfrac{1}{y} + \dfrac{1}{x} = \dfrac{5}{2} \\ \\ \\ \implies \dfrac{2}{y} + \dfrac{2}{x} = 5$

Simplifying eq(2)

$\\ \implies \dfrac{x - y}{xy} = \dfrac{1}{2} \\ \\ \\ \implies \dfrac{x}{xy} - \dfrac{y}{xy} = \dfrac{1}{2} \\ \\ \\ \implies \dfrac{1}{y} - \dfrac{1}{x} = \dfrac{1}{2} \\ \\ \\ \implies \dfrac{2}{y} - \dfrac{2}{x} = 1$

After simplying pair of equations are

$\\ \\ \dfrac{2}{y} + \dfrac{2}{x} = 5 \\ \\ \\ \dfrac{2}{y} - \dfrac{2}{x} = 1$

Substitute 1/y = a , 1/x = b

2a + 2b = 5 → eq(3)

2a - 2b = 1 → eq(4)

Subtracting eq(4) from eq(3)

⇒ 2a + 2b - ( 2a - 2b ) = 5 - 1

⇒ 2a + 2b - 2a + 2b = 4

⇒ 4b = 4

⇒ b = 4/4

⇒ b = 1

Substitute b = 1 in eq(2)

⇒ 2a + 2b = 5

⇒ 2a + 2( 1 ) = 5

⇒ 2a + 2 = 5

⇒ 2a = 5 - 2

⇒ 2a = 3

⇒ a = 3/2

But a = 1/y

⇒ 3/2 = 1/y

⇒ 2/3 = y

⇒ y = 2/3

But b = 1/x

⇒ 1 = 1/x

⇒ x = 1

Note :-

→ I used Elimination method to solve the given question.