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All courses Math III · A-CED.2 9 of 55
Create equations in two or more variables, graph them, and interpret relationships with labels and scales.

Write an equation in two variables from a context

Problem
Write an equation in two variables for this context: a rectangle has width x, length y, and area 60.
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Hint

Identify which formula connects width, length, and area for a rectangle.

For a rectangle, area is found by multiplying width by length.

Solution walkthrough

01

Identify the two variables

\[\text{width}~=~x,\ \text{length}~=~y\]

The problem says the width is \(x\) and the length is \(y\).

02

Use the area formula

\[A~=~\text{xy}\]

A rectangle's area is width times length.

03

Substitute the given area

\[\text{xy}~=~60\]

The area is \(60\), so replace \(A\) with \(60\).

04

State the equation

\[\text{xy}~=~60\]

This equation relates the two variables in the context.

05

State the final answer

\[A~\text{correct}~\text{equation}~\text{is}~\text{xy}~=~60.\]

A correct equation is \(xy=60\).

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Another way

  1. You can start from \(A=lw\) and then replace \(l\) with \(y\), \(w\) with \(x\), and \(A\) with \(60\).

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Common mistake

A common mistake is to add the side lengths and write \(x+y=60\), but area uses multiplication, not addition.