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

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Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely with

x

and

y = 3

when

x = 2

, find

y

when

x = 1

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

y =

_____

Identify general form: Given that $y$ varies inversely with $x$ . Identify the general form of inverse variation. In inverse variation, variables change in opposite directions. Inverse variation: $y = \frac{k}{x}$
Substitute values in equation: We know that $y = 3$ when $x = 2$ . Choose the equation after substituting the values in $y = \frac{k}{x}$ . Substitute $2$ for $x$ and $3$ for $y$ in $y = \frac{k}{x}$ . $3 = \frac{k}{2}$
Solve for k: We found: $\newline$ $3 = \frac{k}{2}$ $\newline$ Solve the equation to find the value of k. $\newline$ To isolate k, multiply both sides by $2$ . $\newline$ $3 \times 2 = \left(\frac{k}{2}\right) \times 2$ $\newline$ $6 = k$
Write inverse variation equation: We have: $\newline$ $k = 6$ $\newline$ Write the inverse variation equation in the form of $y = \frac{k}{x}$ . $\newline$ Substitute $k = 6$ in $y = \frac{k}{x}$ . $\newline$ $y = \frac{6}{x}$
Find $y$ for $x=1$ : Inverse variation equation: $\newline$ $y = \frac{6}{x}$ $\newline$ Find $y$ when $x = 1$ . $\newline$ Substitute $1$ for $x$ in $y = \frac{6}{x}$ . $\newline$ $y = \frac{6}{1}$ $\newline$ $y = 6$

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