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 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 \(6z + 2z + z = 81\).

Solve \(5(y+3) = 4y+10\).

Need more practice? Click here to do some math drill on this topic!

Solve \(5(y+3) = 4y+10\).

Need more practice? Click here to do some math drill on this topic!

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