Algebra – Substitution, Expressions and Equations

Substitution – putting numbers in place of letters

Substituting into an equation:

1. Put the value of the corresponding letter into the equation
2. Use BIDMAS and expand the equation to find the answer

Example:

Q) a = 3 b = 2 c = -4 d = -2

Workout the value of ab – d + c

1. 3 x 2 – (-2) + (-4)
2. Due to BIDMAS rule, workout the multiplication first 3 x 2 = 6
3. Addition must be done before subtraction (-2) + (-4) = -6

          6 – (-6) = 1

A) 12

Tips:

. When two letters are next to each other like ‘ab’ it means a x b

. The rules of BIDMAS means certain calculations must be done before others

. The rules of direct numbers are two like become positive and two unlike signs become negative

. Like signs 3 + (+2) = 5, 3 – (-2) = 5, 3 x (+2) = 6, -3 (-2) = 1.5

. Unlike signs 3 + (-2) = 1, 3 – (+2) = 1, 3 x (-2) = -6, 3 (-2) = -1.5

Expression – a mathematical statement made up of coefficient, variable, operator and constant e.g 9y + 4

Equation – is an expression that is equal to something e.g 9y + 4 = 22

Forming a Expression and Equation:

1. Read the word problem and highlight key information
2. Write the expression/equation in terms of the variable

Example:

I think of a number and call it y. I square the number and subtract 5.

Q) Write an expression for the result

1. Highlight key information
2. y → y² → y² – 5

A) y² – 5

Solving an equation:

1. Put the variables and like terms on the same side 
2. Simplify the equation and solve

Example:

Q) Solve 9y + 4 = 3y + 22

1. Put 3y on the left side by putting 9y on the right-hand side this results in a negative answer which makes the equation harder to solve → 3y – 9y = -6y
2. To bring 3y to the left side subtract 3y from the right side.
3. To keep the equation balanced you must also subtract 3y from the left side → 9y – 3y + 4
4. Subtract 4 from both sides to keep like terms on the same side → 9y – 3y = 22 – 4
5. 9y – 3y = 6y and 22 – 4 = 18
6. 6y = 18 → 6y can also be written as 6 × y. Therefore, to work out what y equals, divide by 6 on both sides → y = 18 ÷ 6

A) y = 3

Equations with two or more variables:

1. Form an equation based on the information given
2. Compare the equations
3. Manipulate the equation based on what you need to find

Example:

5 oranges and 2 apples cost £3.00. 3 oranges and 1 apple cost £2.20.

Q) What is the price of 4 oranges and 2 apples?

1. 5o + 2a = 3 (equation 1) and 3o + a = 2.20 (equation 2)
2. Equation 1 – Equation 2 = 2o + a = 0.8 (equation 3)
3. (equation 3) x 2 = (2o + a) x 2 = 4o + 2a → 0.8 x 2 = 1.6

A) £1.60