Question

Solve this:-
$\frac{1}{x} + \frac{1}{y} = 14$
$\frac{1}{x} - \frac{1}{y} = 4$

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Answer 1

Answer:

$\mathtt\red{LET:-}$

$\mathtt{ \frac{1}{x} = p}$

$\mathtt{ \frac{1}{y} = q }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\red{SOLUTION:-}$

$\mathtt\red{NOW}$

$\mathtt{ \: \: \: p + q = 14} \\ \mathtt{p + q = 4}$

$\mathtt\red{BY \: ELIMINATION \: METHOD}$

$\mathtt{ \: \: \: p + q = 14} \\ \mathtt{p - q = 4} \\ \mathtt{2p \: \: \: \: \: \: \: = 18} \\ \mathtt{p \: \: \: \: \: \: \: \: \: \: = \frac{18}{2} } \\ \mathtt{p \: \: \: \: \: \: \: = 9}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\red{IN \: EQUATION \: 2}$

$\mathtt{p + q = 14} \\ \mathtt{9 + q = 14} \\ \mathtt{q \: \: \: \: \: \: = 5}$

$\mathtt\red{NOW}$

$\mathtt{ \frac{1}{x} = p} \\ \mathtt{ \frac{1}{x} = 9 } \\ \mathtt{9x = 1} \\ \mathtt{x = \frac{1}{9} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{ \frac{1}{y} = q} \\ \mathtt{ \frac{1}{y} = 5} \\ \mathtt{5y = 1} \\ \mathtt{y = \frac{1}{5} }$

Answer 2

Step-by-step explanation:

OLUTION:−

\mathtt\red{NOW}NOW

\begin{gathered} \mathtt{ \: \: \: p + q = 14} \\ \mathtt{p + q = 4}\end{gathered}

p+q=14

p+q=4

\mathtt\red{BY \: ELIMINATION \: METHOD}BYELIMINATIONMETHOD

\begin{gathered} \mathtt{ \: \: \: p + q = 14} \\ \mathtt{p - q = 4} \\ \mathtt{2p \: \: \: \: \: \: \: = 18} \\ \mathtt{p \: \: \: \: \: \: \: \: \: \: = \frac{18}{2} } \\ \mathtt{p \: \: \: \: \: \: \: = 9}\end{gathered}

p+q=14

p−q=4

2p=18

p=

2

18

p=9

\: \: \: \: \: \: \: \: \: \: \: \: \:

\mathtt\red{IN \: EQUATION \: 2}INEQUATION2

\begin{gathered} \mathtt{p + q = 14} \\ \mathtt{9 + q = 14} \\ \mathtt{q \: \: \: \: \: \: = 5}\end{gathered}

p+q=14

9+q=14

q=5

\mathtt\red{NOW}NOW

\begin{gathered} \mathtt{ \frac{1}{x} = p} \\ \mathtt{ \frac{1}{x} = 9 } \\ \mathtt{9x = 1} \\ \mathtt{x = \frac{1}{9} }\end{gathered}

x

1

=p

x

1

=9

9x=1

x=

9

1

\: \: \: \: \: \: \: \: \: \: \: \: \:

\begin{gathered} \mathtt{ \frac{1}{y} = q} \\ \mathtt{ \frac{1}{y} = 5} \\ \mathtt{5y = 1} \\ \mathtt{y = \frac{1}{5} }\end{gathered}

y

1

=q/y1

=5

5y=1

y= 1/5