Question Find the solutions for $y$ given the equations $x=1/y$ , $y=x$ , $y=1$ , $y=1/x$ , and $y=1/x^2$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $x = \frac{1}{y}$ .
2. We need to solve for $y$ .
3. We are given multiple choice options for the value of $y$ .

STEP 2

To solve for $y$ , we need to isolate $y$ on one side of the equation. We can do this by taking the reciprocal of both sides of the equation.
$\frac{1}{x} = \frac{1}{\frac{1}{y}}$

STEP 3

Simplify the right side of the equation by recognizing that taking the reciprocal of a reciprocal gives us the original value.
$\frac{1}{x} = y$

STEP 4

Now that we have isolated $y$ , we can compare our result to the given options to find the correct one.

STEP 5

The correct option that matches our result $\frac{1}{x} = y$ is:
$y = \frac{1}{x}$
Therefore, the solution is $y = \frac{1}{x}$ .

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Question Find the solutions for $y$ given the equations $x=1/y$ , $y=x$ , $y=1$ , $y=1/x$ , and $y=1/x^2$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $x = \frac{1}{y}$ .
2. We need to solve for $y$ .
3. We are given multiple choice options for the value of $y$ .

STEP 2

To solve for $y$ , we need to isolate $y$ on one side of the equation. We can do this by taking the reciprocal of both sides of the equation.
$\frac{1}{x} = \frac{1}{\frac{1}{y}}$

STEP 3

Simplify the right side of the equation by recognizing that taking the reciprocal of a reciprocal gives us the original value.
$\frac{1}{x} = y$

STEP 4

Now that we have isolated $y$ , we can compare our result to the given options to find the correct one.

STEP 5

The correct option that matches our result $\frac{1}{x} = y$ is:
$y = \frac{1}{x}$
Therefore, the solution is $y = \frac{1}{x}$ .

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Question Find the solutions for yyy given the equations x=1/yx=1/yx=1/y, y=xy=xy=x, y=1y=1y=1, y=1/xy=1/xy=1/x, and y=1/x2y=1/x^2y=1/x2.

Studdy Solution

STEP 1

Assumptions1. We are given the equation x=1yx = \frac{1}{y}x=y1​.2. We need to solve for yyy.3. We are given multiple choice options for the value of yyy.

STEP 2

To solve for yyy, we need to isolate yyy on one side of the equation. We can do this by taking the reciprocal of both sides of the equation.1x=11y\frac{1}{x} = \frac{1}{\frac{1}{y}}x1​=y1​1​

STEP 3

Simplify the right side of the equation by recognizing that taking the reciprocal of a reciprocal gives us the original value.1x=y\frac{1}{x} = yx1​=y

STEP 4

Now that we have isolated yyy, we can compare our result to the given options to find the correct one.

STEP 5

The correct option that matches our result 1x=y\frac{1}{x} = yx1​=y is:y=1xy = \frac{1}{x}y=x1​Therefore, the solution is y=1xy = \frac{1}{x}y=x1​.

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Question Find the solutions for $y$ given the equations $x=1/y$ , $y=x$ , $y=1$ , $y=1/x$ , and $y=1/x^2$ .

Assumptions
1. We are given the equation $x = \frac{1}{y}$ .
2. We need to solve for $y$ .
3. We are given multiple choice options for the value of $y$ .

To solve for $y$ , we need to isolate $y$ on one side of the equation. We can do this by taking the reciprocal of both sides of the equation.
$\frac{1}{x} = \frac{1}{\frac{1}{y}}$

Simplify the right side of the equation by recognizing that taking the reciprocal of a reciprocal gives us the original value.
$\frac{1}{x} = y$

Now that we have isolated $y$ , we can compare our result to the given options to find the correct one.

The correct option that matches our result $\frac{1}{x} = y$ is:
$y = \frac{1}{x}$
Therefore, the solution is $y = \frac{1}{x}$ .