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Year 7AC9M7A01

Substituting into Formulas

Recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown.

Substitution means swapping a letter for a number. Use brackets when you do it and most substitution errors disappear.

Method

Replace the letter with the number in brackets
x=4 ⇒ 3x=3(4)x = 4 \ \Rightarrow\ 3x = 3(4)
Brackets stop $3x$ becoming $34$.
Follow the order of operations
Brackets, indices, then multiply and divide, then add and subtract.
A negative substituted into a square is positive
(−3)2=9(-3)^2 = 9
Without the brackets you would get $-9$, which is wrong.

Worked example

e.g. Find the value of 5x−2y when x=4 and y=3\text{Find the value of } 5x - 2y \text{ when } x = 4 \text{ and } y = 3
  1. Write the expression out again.5x−2y5x - 2y
  2. Replace each letter with its number in brackets.5(4)−2(3)5(4) - 2(3)
  3. Do the multiplications first.20−620 - 6
  4. Then the subtraction.1414
  5. Write the answer.5x−2y=145x - 2y = 14

Practice

Substitute with brackets, then follow the order of operations.

1
Find 3a+2 when a=5\text{Find } 3a+2 \text{ when } a = 5
Answer1717
2
Find x2−1 when x=6\text{Find } x^2 - 1 \text{ when } x = 6
Answer3535
3
Find 2(m+n) when m=3, n=4\text{Find } 2(m+n) \text{ when } m=3,\ n=4
Answer1414
4
Find A=12bh when b=10, h=6\text{Find } A = \tfrac{1}{2}bh \text{ when } b=10,\ h=6
Answer3030
5
Find x2 when x=−4\text{Find } x^2 \text{ when } x = -4
Answer(−4)2=16(-4)^2 = 16
6
Find V=lwh when l=4, w=3, h=2\text{Find } V = lwh \text{ when } l=4,\ w=3,\ h=2
Answer2424
7
In P=2l+2w, find l when P=30 and w=5\text{In } P = 2l + 2w, \text{ find } l \text{ when } P=30 \text{ and } w=5
Answerl=10l = 10
Next step
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