An equation with one unknown has one variable. For example, $$2x + 1 = 5$$ is a one variable equation. However, $$2x + y = 5$$ is a two variables equation.

A linear equation refers to the equation that  interprets as a line  when plotted on a graph. Basically any equations with variables not more than the power of 1 is linear. For example, $$2x + y = 5$$ is a first power equation which is linear, but $$2x + y^2 = 5$$ is NOT linear because $$y$$ has the second power.

### Graph of $$2x + y = 5$$

To solve a linear equation with one unknown(variable), the unknown should be isolated on one side of the equation.

To do this, just add / subtract / multiply / divide the same number on both sides of an equation.

Example Solve $$9x + 6x + 3 = 12$$.
Solution  $$9x + 6x + 3 = 12 \\ \, \\ \underbrace{(9x + 6x)}_{\substack{\text{Combine} \\ \text{Like-Terms}}} + 3 = 12 \\ \, \\ (9x + 6x) + \underbrace{3 {\color{red}{-3}}}_{\substack{\text{Subtract} \\ \text{the same} \\ \text{number}}} = \underbrace{12 {\color{red}{-3}}}_{\substack{\text{Subtract} \\ \text{the same} \\ \text{number}}} \\ \, \\ 15x = 9 \\ \, \\ x = \dfrac{15}{9}$$

Solve $$6z + 2z + z = 81$$.
$$6z + 2z + z = 81 \\ 9z = 81 \\ \, \\ \underbrace{ \dfrac{9z}{{\color{red}{9}}} }_{\substack{\text{Divide} \\ \text{the same} \\ \text{number}}} = \underbrace{ \dfrac{81}{{\color{red}{9}}} }_{\substack{\text{Divide} \\ \text{the same} \\ \text{number}}} \\ \, \\ z = 9$$
Solve $$5(y+3) = 4y+10$$.
$$\underbrace{ 5(y+3) }_{\substack{\text{Expand}}} = 4y+10 \\ \, \\ 5y+15 = 4y + 10 \\ \, \\ 5y+15 \underbrace{{\color{red}{-4y}}}_{\substack{\text{Subtract} \\ \text{the same} \\ \text{number}}} = 4y + 10 \underbrace{{\color{red}{-4y}}}_{\substack{\text{Subtract} \\ \text{the same} \\ \text{number}}} \\ \, \\ 5y – 4y + 15 = 10 \\ 5y – 4y + 15 {\color{red}{-15}} = 10 {\color{red}{-15}} \\ 5y – 4y = 10 – 15 \\ y = -5$$