Linear Equations Worksheet With Answers Page 4
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212. Solving a linear equation.
To solve a linear equation we try to make the unknown quantity the subject of the equation.
This means we attempt to obtain the unknown quantity on its own on the left-hand side. To do
this we may apply the same five rules used for transposing formulae given in Chapter 1 Block
7. These are given again here.
Key Point
Operations which can be used in the process of solving a linear equation:
• add the same quantity to both sides
• subtract the same quantity from both sides
• multiply both sides by the same quantity
• divide both sides by the same quantity
• take functions of both sides; for example square both sides.
A useful summary of these rules is ‘whatever we do to one side of an equation we must also do
to the other’.
Example
Solve the equation x + 14 = 5.
Solution
Note that by subtracting 14 from both sides, we leave x on its own on the left. Thus
x + 14 − 14 = 5 − 14
x = −9
Hence the solution of the equation is x = −9. It is easy to check that this solution is correct
by substituting x = −9 into the original equation and checking that both sides are indeed the
same. You should get into the habit of doing this.
Example
Solve the equation 19y = 38.
Solution
In order to make y the subject of the equation we can divide both sides by 19:
19y = 38
19y
38
=
19
19
38
cancelling 19’s gives
y =
19
so
y = 2
Hence the solution of the equation is y = 2.
4
Engineering Mathematics: Open Learning Unit Level 0
3.1: Polynomial Equations, inequalities
and partial fractions
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