Question

And also value of p
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Answer 1

Step-by-step explanation:

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Answer 2

Question :-

$\rm{solve \: \frac{1}{q} + \frac{1}{p} = 7 \: and \: \frac{2}{q} - \frac{3}{p} = - 1}$

Solution :-

Given :

$\sf{☯ \: \frac{1}{q} + \frac{1}{p} = 7 \: \: \: \: - - - \{ equation \:(1) \} }$

$\sf{☯ \: \frac{2}{q} - \frac{3}{p} = - 1 \: \: \: \: - - - \{ equation \:(2) \} }$

In the given two equation we have fractions, then we multiply by cross in those equations and then find the values.

From equation (1)

$\sf:\longmapsto{ \frac{1}{q} + \frac{1}{p} = 7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{p + q = 7} \: \: \: \: \: \: --- \{equation \: (3) \}$

From equation (2)

$\sf:\longmapsto{ \frac{2}{q} - \frac{3}{p} = - 1 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{2p - 3p = - 1} \: \: \: \: \: \: - - - \{equation \: (4) \}$

Multiply equation (3) by 3 we get,

$\sf{➡ \: 3p + 3q = 21 \: \: \: \: - - - \{equation \: (5) \} }$

Add equation (5) and (4)

$\sf:\longmapsto{3p + 3q + (2p - 3q) = 21 + ( - 1)} \\ \\ \sf:\longmapsto{3p + 2p + 3q - 3q = 21 - 1} \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{5p = 20} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{p = 4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Substitute p = 4 in (3)

$\sf:\longmapsto{p + q = 7} \\ \\\sf:\longmapsto{4 + q = 7} \\ \\\sf:\longmapsto{q = 7 - 4} \\ \\\bf:\longmapsto \red{q = 3} \: \: \: \: \: \:$

The value of q is 3.

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