Equations

Ontario 10 Applied (MFM2P)

Rearrange a linear equation

Lesson

Changing the subject of a formula is an important skill to learn. It can come in very handy when you know the value of one algebraic symbol but not another. Basically, the subject of an equation is the variable that is by itself on one side on the equals sign and it usually is at the start of the formula.

For example, in the formula $A=pb+y$`A`=`p``b`+`y`, $A$`A` is the subject because it is by itself on the left hand side of the equals sign.

We sort of started changing the subject of equations when we learnt to solve equations because we took steps to get the variable by itself, for example we made $x$`x` the subject of equations. We can make any term in an equation the subject, even if it starts off as the denominator of a fraction. When we're changing the subject of a formula, we often have more than one variable but we still use a similar process.

- Group any like terms
- Simplify using the inverse of addition or subtraction.
- Simplify further by using the inverse of multiplication or division.

Make $x$`x` the subject of the following equation:

$y=\frac{x}{4}$`y`=`x`4

Make $m$`m` the subject of the following equation:

$\frac{m}{y}=gh$`m``y`=`g``h`

Make $m$`m` the subject of the following equation:

$y=6mx-9$`y`=6`m``x`−9

Determine the value of a variable in the first degree, using a formula