# 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

 y² (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