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Equation of a Line Perpendicular to a Given Line

Solve the fol...

Question

Solve the following systems of equations:

$\frac{1}{3 x + y} + \frac{1}{3 x - y} = \frac{3}{4} \frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = - \frac{1}{8}$

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Solution

The given equations are:

Let and then equations are

…

…

Multiply equation by and add both equations, we get

Put the value of in equation, we get

Then

…

…

Add both equations, we get

Put the value of in equation we get

Hence the value of and

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Q. Solve for x and y:

\frac{1}{(3 x + y)} + \frac{1}{(3 x - y)} = \frac{3}{4} \frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}

\frac{1}{3 x + y} + \frac{1}{3 x - y} = \frac{3}{4}

\frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}

x

y

\frac{1}{3 x + y} + \frac{1}{3 x - y} = \frac{3}{4}

\frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}

Q. Solve the following systems of equations:

\frac{6}{x + y} = \frac{7}{x - y} + 3 \frac{1}{2 (x + y)} = \frac{1}{3 (x - y)'}

where x + y ≠ 0 and x − y ≠ 0

Q. Solve the following pair of equations for

x

y \frac{15}{x - y} + \frac{22}{x + y} = 5

\frac{40}{x - y} + \frac{55}{x + y} = 13 x \neq y

x \neq - y

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