# 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

Formulate the following problems as a pair of equations, and hence find their solutions:

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

#### Solution

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The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju

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Solve \frac{1}{x+y}+\frac{2}{x-y}=2\text{ and }\frac{2}{x+y}-\frac{1}{x-y}=3 where, x + y ≠ 0 and x – y ≠ 0

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Solve the following pair of linear equations

px + qy = p − q

qx − py = p + q

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Solve the following simultaneous equations:

7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33

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

4/x + 3y = 14

3/x - 4y = 23

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