Question

1/2x-1/y= -1 and 1/x + 1/2y = 8 solve the problem by substitution method

Answer 1

Hi there !!

Look at the attachment.

x=1/6 and y =1/4

Verification :-

1/2x-1/y= -1 and 1/x + 1/2y = 8 (substitute x and y)

$\frac{1}{ \frac{1}{3} } - \frac{1}{ \frac{1}{4} } \\ \\ = \frac{3}{1} - \frac{4}{1} \\ \\ = - 1$

This satisfied L. H. S = R.H.S

Thankyou :)

Answer 2

The value of x is $x=\frac{1}{6}$ and the value of $y=\frac{1}{4}$

Step-by-step explanation:

Consider the provided equation.

$\frac{1}{2x}-\frac{1}{y}=\:-1$ and $\:\frac{1}{x}\:+\:\frac{1}{2y}\:=\:8$

$\frac{1}{2x}=-1+\frac{1}{y}$

$\frac{1}{2x}=\frac{-y+1}{y}$

$x=-\frac{y}{2\left(-1+y\right)}$

Substitute the value of x in $\:\frac{1}{x}\:+\:\frac{1}{2y}\:=\:8$

$\frac{1}{-\frac{y}{2\left(-1+y\right)}}+\frac{1}{2y}=8$

$-\frac{2\left(-1+y\right)}{y}+\frac{1}{2y}=8$

Multiply by 2y.

$-4\left(-1+y\right)+1=16y$

$-4y=16y-5$

$y=\frac{1}{4}$

Substitute the value of y in $x=-\frac{y}{2\left(-1+y\right)}$.

$x=-\frac{\frac{1}{4}}{2\left(-1+\frac{1}{4}\right)}$

$x=\frac{1}{4\cdot \:2\left(-1+\frac{1}{4}\right)}$

$x=-\frac{1}{8\left(-\frac{3}{4}\right)}$

$x=\frac{1}{6}$

Hence, the value of x is $x=\frac{1}{6}$ and the value of $y=\frac{1}{4}$

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