Worked example 1 Study the following equations and fi nd the value of a and b that would make each equation true. (i) a+ 12 = 17
(ii) 20 – b = 5 Solution (ii) ✗ ✓ Worked example 2
The scales are balanced in each of the following diagrams. Find the unknown values and explain how you found your answer.
Solution (i)
? = 5
1 box = 5 Answer: 1 box = 5 units
(ii) ? 3 =
1 box + 3 = 10 1b + 3 = 10
To get b on its own (solve for b), we must subtract 3 from both sides.
1b + 3 − 3 = 10 − 3 1b = 7
Answer: 1 box = 7 units 10
2 boxes + 4 = 16 2b + 4 = 16
2b + 4 − 4 = 16 − 4 (subtract 4 from both sides)
2b = 12 2b
b = 6 Answer: 1 box = 6 units
Solving linear equations Identify the unknown variable (or the variable whose value needs to be found).
1 2
Then we must get the variable on its own. Whatever you do to one side of an equation, you must do exactly the same thing to other side of that equation, or it will not stay equal. So if you add 4 to the left side of an equation, you need to add 4 to the right side too.
3 Verify your answer by substituting it back into the equation.
Fundamental rule in Maths Whatever operation you do (add, subtract, divide, multiply) to one side of an equation, you must also do to the other. This way, both sides of the equation remain equal.