Solve the following pair of equations.6x+4y=20 and 9x-7y=10.5

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Uploaded: 2023-05-17T14:00:00.000Z
Duration: 20 min 32 s
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A
$x = \frac{3}{7}, y = \frac{2}{3}$
B
$x = \frac{2}{5}, y = \frac{2}{3}$
C
$x = \frac{5}{7}, y = \frac{1}{3}$
D
$x = \frac{2}{5}, y = \frac{1}{7}$

Solution:

Given equations are,

\frac{6}{x} + \frac{4}{y} = 20

and,

\frac{9}{x} - \frac{7}{y} = 10.5

.
Let

\frac{1}{x} = a

and

\frac{1}{y} = b

.
So, the original equations will reduce to,

6 a + 4 b = 20

...

(1)

and,

9 a - 7 b = 10.5

...

(2)

Multiplying

(1)

7

, we get,

42 a + 28 b = 140

...

(3)

Multiplying

(2)

4

, we get,

36 a - 28 b = 42

...

(4)

Adding

(3)

and

(4)

78 a = 182

⇒

a = \frac{182}{78}

⇒

a = \frac{14}{6}

⇒

a = \frac{7}{3}

Substituting

a = \frac{7}{3}

(1)

, we get,

14 + 4 b = 20

⇒

4 b = 6

⇒

b = \frac{6}{4}

⇒

b = \frac{3}{2}

Now,

a = \frac{1}{x}

,
So,

x = \frac{1}{a}

.
⇒

x = \frac{3}{7}

⇒

b = \frac{1}{y}

,
So,

y = \frac{1}{b}

.
⇒

y = \frac{2}{3}

⇒

x = \frac{3}{7}, y = \frac{2}{3}

.
Hence, the correct option is 1.

Solve the following pair of equations. $\frac{6}{x} + \frac{4}{y} = 20$ and $\frac{9}{x} - \frac{7}{y} = 10.5$

Solution:

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