Question

$\frac{4}{x} + 3y = 14 \\ \frac{3}{x} - 4y = 23$
answer it ​

Answer 1

$\frac{4}{x} + 3y = 14$

$\frac{3}{x} - 4y = 23$

____________ [ GIVEN ]

• We have to find the value of x and y.

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• Let $\frac{1}{x}$ = a and $y$ = b.

→ 4a + 3b = 14 ________ (eq 1)

→ 3a - 4b = 23 _________ (eq 2)

Now;

Multiply (eq 1) with 3 and (eq 2) with 4

→ 4a + 3b = 14 (×3)

→ 12a + 9b = 42 ________ (eq 3)

→ 3a - 4b = 23 (×4)

→ 12a - 16b = 92 _________ (eq 4)

Subtract (eq 4) from (eq 3)

→ 12a + 9b - (12a - 16b) = 42 - 92

→ 12a - 12a + 9b + 16b = - 50

→ 25b = - 50

→ b = - 2

Put value of b in (eq 1)

→ 4a + 3(-2) = 14

→ 4a - 6 = 14

→ 4a = 20

→ a = 5

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Now..

→ $\dfrac{1}{x}$ = a

→ $\dfrac{1}{x}$ = 5

→ $x\:=\:\dfrac{1}{5}$

Similarly

→ $y\:=\:b$

→ $y\:=\:-\:2$

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$\huge{\bold{x \:= \:1/5 \:and}}$

$\huge{\bold{y \:= \:-2}}$

____________ [ ANSWER ]

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✡ VERIFICATION :

From above calculations we get x = 1/5 and b = -2

Put value of x and y in this equation : 4/x + 3y = 14

=> 4/(1/5) + 3(-2) = 14

=> 20 - 6 = 14

=> 14 = 14

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