Solve the following pair of equations.9x-4y=8 and 13x+7y=101.

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Uploaded: 2023-05-17T14:00:00.000Z
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A
$x = \frac{2}{3}, y = \frac{4}{3}$
B
$x = \frac{1}{4}, y = \frac{1}{7}$
C
$x = \frac{5}{4}, y = \frac{2}{5}$
D
$x = \frac{3}{2}, y = \frac{6}{5}$

Solution:

Given equations are

\frac{9}{x} - \frac{4}{y} = 8

and

\frac{13}{x} + \frac{7}{y} = 101

.
The equation

\frac{9}{x} - \frac{4}{y} = 8

can be simplified as,

\frac{9}{x} - \frac{4}{y} = 8

\Rightarrow \frac{9 y - 4 x}{xy} = 8

\Rightarrow 9 y - 4 x = 8 xy . . . . . . . . . (1)

The equation

\frac{13}{x} + \frac{7}{y} = 101

can be simplified as,

\frac{13}{x} + \frac{7}{y} = 101

\Rightarrow \frac{13 y + 7 x}{xy} = 101

\Rightarrow 13 y + 7 x = 101 xy . . . . . . . . . (2)

Multiply the equation (1) by

7

and equation (2) by

4

.
Then we get the equations,

63 y - 28 x = 56 xy . . . . . . . . . (3)

52 y + 28 x = 404 xy . . . . . . . . . (4)

Add equations 3 and 4 to eliminate

x

, because the coefficients of

x

are the opposite. So, we get,

(63 y + 52 y) + (- 28 x + 28 x) = 56 xy + 404 xy

⇒

115 y = 460 xy

⇒

115 = 460 x

⇒

x = \frac{115}{460}

⇒

x = \frac{1}{4}

Substituting this value of

x

in the equation (1), we get,

9 y - 4 (\frac{1}{4}) = 8 (\frac{1}{4}) y

\Rightarrow 9 y - 1 = 2 y

\Rightarrow 9 y - 2 y = 1

\Rightarrow 7 y = 1

\Rightarrow y = \frac{1}{7}

The solution of the equations is

x = \frac{1}{4}, y = \frac{1}{7}

.
Hence, the correct option is 2.

Solve the following pair of equations. $\frac{9}{x} - \frac{4}{y} = 8$ and $\frac{13}{x} + \frac{7}{y} = 101$ .

Solution:

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