# Solution - Equations Reducible to a Pair of Linear Equations in Two Variables

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ConceptEquations Reducible to a Pair of Linear Equations in Two Variables

#### Question

Solve the following system of equations \frac { 1 }{ 2x } – \frac { 1 }{ y } = – 1; \frac { 1 }{ x } + \frac { 1}{ 2y } = 8

#### Solution

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Solve \frac { 2 }{ x } + \frac { 1 }{ 3y } = \frac { 1}{ 5 }; \frac { 3 }{ x } + \frac { 2 }{ 3y } = 2 and also find ‘a’ for which y = ax – 2

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One says, "Give me a hundred, friend! I shall then become twice as rich as you". The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II)

[Hint: x + 100 = 2 (y − 100), y + 10 = 6(x − 10)]

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Solve the following pairs of equations by reducing them to a pair of linear equations

2/sqrtx +3/sqrty = 2

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Solve the following systems of equations

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\frac{1}{u} + \frac{1}{v} = \frac{36}{5}

(ii)  \frac{11}{v} – \frac{7}{u} = 1

\frac{9}{v} + \frac{4}{u} = 6

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Solve the following pair of linear equations

px + qy = p − q

qx − py = p + q

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#### Reference Material

Solution for concept: Equations Reducible to a Pair of Linear Equations in Two Variables. For the course 8th-10th CBSE
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