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Linear equations

A linear equation is an equation that depends only on the variable and not on any power. It only involves linear functions of the variable.

The following equations are linear: $$$ \Tred{x}-1 = 0, \quad 3\Tred{ t } + 2 = -2, \quad \frac{\Tred{y}}{2} + \frac{4}{5} = -\frac{\sqrt{3}}{7}$$$

The following equations are not linear: $$$ \Tred{x}^2 = 1,\quad \sqrt{\Tred{t}} - 1 = 0,\quad \frac{1}{\Tred{y}} + \frac{1}{\Tred{y}-1} = 1$$$

The general form of a linear equation is $$$ \Tgreen{a} \Tred{x} + \Tgreen{b} = \Tgreen{c}$$$ for numbers $$\Tgreen{a}\ne0$$, $$\Tgreen{b}$$ and $$\Tgreen{c}$$.