Simplifying formulas » Rearranging and substituting formulas

Rearranging formulas

You can use the balance method to rearrange a formula.
In formula q = 5p + 7 is q expressed in terms of p.
In formula a = 4b² + 1 is a expressed in terms of b.

Example 1
Given is the formula 5q + 20p = 45
Rearrange this formula so q is expressed in terms of p.

Answer:

5`q` + 20`p`	= 45
5`q`	= –20`p` + 45
`q`	= –4`p` + 9

Example 2
Given is the formula 2(4a – 6) + 5b = 4
Rearrange this formula so a is expressed in terms of b.

Answer:

2(4`a` – 6) + 5`b`	= 4
8`a` – 12 + 5`b`	= 4
8`a`	= –5`b` + 16
`a`	= –58`b` + 2

Substituting formulas

Substituting is change a variable in a formula with another formula.
After you substituted you shorten the formula.
Important: The formule you are substituting will be between brackets.

Example 1
Substitute formula B into formula A.
A: y = 6t + 12 and B: t = 3x + 4

Answer:

`y`	= 6`t` + 12
`y`	= 6(3`x` + 4) + 12
`y`	= 18`x` + 24 + 12
`y`	= 18`x` + 36

Example 2
Substitute formula B into formula A.
A: p = 3q – 2 and B: q = 4a + 7

Answer:

`p`	= 3`q` – 2
`p`	= 3(4`a` + 7) – 2
`p`	= 12`a` + 21 – 2
`p`	= 12`a` + 19