Using the following equations:4x+6y=10 ; 1x-6y=5,find the value of p if p=5x.

Given that,

\frac{4}{x} + 6 y = 10; \frac{1}{x} - 6 y = 5

and

p = 5 x

.
Elimination method on adding equation 1 and 2,
Adding the two equations,

\frac{4}{x} + 6 y + \frac{1}{x} - 6 y = 10 + 5

\Rightarrow \frac{4}{x} + \frac{1}{x} = 15

\Rightarrow \frac{4 + 1}{x} = 15

\Rightarrow \frac{5}{x} = 15

\Rightarrow 5 = 15 x

\Rightarrow x = \frac{5}{15}

\Rightarrow x = \frac{1}{3}

Substituting x value in equation

\frac{4}{x} + 6 y = 10

\Rightarrow \frac{4}{\frac{1}{3}} + 6 y = 10

\Rightarrow \frac{4}{3} + 6 y = 10

\Rightarrow 6 y = 10 - \frac{4}{3}

\Rightarrow 6 y = \frac{30 - 4}{3}

\Rightarrow 6 y = \frac{26}{3}

\Rightarrow y = \frac{26}{3} \times 6

\Rightarrow y = \frac{156}{3}

\Rightarrow y = 52

Now, substituting x value in

p = 5 x

x = \frac{1}{3}

so,

\Rightarrow p = 5 \times \frac{1}{3}

\Rightarrow p = \frac{5}{3}

Thus, the value of

p = \frac{5}{3}

.
Therefore, the correct option is 4.

Using the following equations: $\frac{4}{x} + 6 y = 10; \frac{1}{x} - 6 y = 5$ ,

find the value of p if $p = 5 x$ .