Linear Equations Worksheet With Answers Page 2
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211. Linear equations
Key Point
A linear equation is an equation of the form
ax + b = 0
a = 0
where a and b are known numbers and x represents an unknown quantity which we must find.
In the equation ax + b = 0, the number a is called the coefficient of x, and the number b is
called the constant term.
The following are examples of linear equations
1
−2x + 3 = 0,
−
x − 3 = 0
3x + 4 = 0,
2
√
2
Note that the unknown, x, appears only to the first power, that is as x, and not as x
,
x,
1/2
x
etc. Linear equations often appear in a nonstandard form, and also different letters are
sometimes used for the unknown quantity. For example
1
3t − 7 = 17,
1 −
2x = x + 1
13 = 3z + 1,
y = 3
2
are all examples of linear equations. Where necessary the equations can be rearranged and
written in the form ax + b = 0. We will explain how to do this later in this Block.
Now do this exercise
Which of the following are linear equations and which are not linear?
(a) 3x + 7 = 0, (b) −3t + 17 = 0,
2
(c) 3x
+ 7 = 0,
(d) 5x = 0
The equations which can be written in the form ax + b = 0 are linear.
Answer
To solve a linear equation means to find the value of x that can be substituted into the equation
so that the left-hand side equals the right-hand side. Any such value obtained is known as a
solution or root of the equation and the value of x is said to satisfy the equation.
Consider the linear equation 3x − 2 = 10.
Example
(a)
Check that x = 4 is a solution.
(b)
Check that x = 2 is not a solution.
2
Engineering Mathematics: Open Learning Unit Level 0
3.1: Polynomial Equations, inequalities
and partial fractions
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