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If $y$ varies inversely with $x$ and $y = 2$ when $x = 3$ , find $y$ when $x = 1$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

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Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely with

x

and

y = 2

when

x = 3

, find

y

when

x = 1

.

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

_____

Given Inverse Variation Equation: Given that $y$ varies inversely with $x$ , we can write the inverse variation equation as $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Substitute Values to Find Constant: We know that $y = 2$ when $x = 3$ . Substitute these values into the inverse variation equation to find the constant $k$ . $2 = \frac{k}{3}$
Calculate Constant: To find $k$ , multiply both sides of the equation by $3$ . $2 \times 3 = k$ $k = 6$
Complete Inverse Variation Equation: Now that we have the constant of variation, we can write the complete inverse variation equation as $y = \frac{6}{x}$ .
Find $y$ for $x=1$ : To find $y$ when $x = 1$ , substitute $1$ for $x$ in the equation $y = \frac{6}{x}$ . $\newline$ $y = \frac{6}{1}$ $\newline$ $y = 6$

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