Solving Linear Equations

 

Linear Equation:

A mathematical expression that has an equal sign and linear expressions, variable  and  a number that you don't know, often represented by "x" or "y" forms a linear equation.

Variable(s) in linear expressions

  • Cannot have exponents (or powers)

For example: xsquared or x2

  • Cannot multiply or divide each other

For example: "x" times "y" or xy; "x" divided by "y" or x/y

  • Cannot be found under a root sign or square root sign (sqrt)

For example: √x or the "square root x"; sqrt (x)

Linear Expression:

A mathematical statement that performs functions of addition, subtraction, multiplication, and division.

Examples of linear expression

  • x + 4
  • 2x + 4
  • 2x + 4y

Examples of Non Linear Expressions

 

(no exponents on variables)

6xy + 4

(can't multiply two variables)

4x / 8y

(can't divide two variables)

√y

(no square root sign on variables)

Example :

Find x if: 4x + 8 = 20

1.

Isolate "x" to one side of the equation 
by subtracting 4 from both sides:

4x + 8 - 8 = 20 - 8

4x = 12

2.

Divide both sides by 2:

4x / 2 = 12 / 2

2x = 6

X=3

3.

Check your work with the original equation:

4x + 8 = 20
(4 * 3) + 8 = 20
12 + 8 = 20

Example :

Find x if: 8x - 4y = 8
(using more than one variable)

1.

First step is to isolate "x" 
to one side of the equation by adding 4y to both sides:

4x - 4y + 4y = 8 + 4y
4x = 8 + 4y

2.

Second step is to divide both sides by 4:

4x / 4 = (8 + 4y) / 4
x = 2 + y

3.

Check your work with the original equation:

4 * (2 + y) - 4y = 8
8 + 4y - 4y = 8
8 = 8