Solve a formula for a variable

Warm-up

Three quick questions from earlier lessons.

Discover

A rectangle has perimeter $P = 2\ell + 2w$ . You know $P$ and $\ell$ . Which formula gives $w$ directly?

$w = \dfrac{P - 2\ell}{2}$
$w = P - \dfrac{2\ell}{2}$

Key idea

Solve for a letter as you solve for $x$ .

To solve for a variable, treat the other letters as numbers: use the same moves as for a number equation until that variable is alone. Divide every term on the other side.

Worked example

Solve $3x + 2y = 12$ for $y$ .

2y = 12 - 3x

Subtract 3x.

y = \dfrac{12 - 3x}{2}

Divide both terms by 2.

Your turn, guided

Your turn: $y = 4x + 8$ . Solve for $x$ .

x = \dfrac{y - 8}{4}

Subtract 8, divide by 4.

Practice ★

A car moves at 2 miles per minute, so $d = 2t$ . Solve for $t$ . $t = \;?$
A car moves at 4 miles per minute, so $d = 4t$ . Solve for $t$ . $t = \;?$

Solve $7x + 9y = 23$ for $y$ . $y = \;?$

Watch out!

Practice ★★

Solve $y = 9x + 3$ for $x$ . $x = \;?$
Solve $y = 2x + 4$ for $x$ . $x = \;?$

Exit ticket

Three questions to check you have got it.

Solve $7x + 9y = 23$ for $y$ . $y = \;?$
Solve $7x + 5y = 13$ for $y$ . $y = \;?$
Solve $7x + 8y = 7$ for $y$ . $y = \;?$

Summary card

Solving for a variable

Same moves as with numbers; the other letters are just numbers you do not know.

Watch out: divide every term.

End of the lesson

Next lesson: Linear equations in two variables and their graphs Back to the chapter

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