What is a linear equation?
As the term suggests, linear equations have to do with lines; and in algebra, a linear equation means certain equations (or functions) whose graph is a line (for an extensive explanation of graphs, see “Geometry and Trigonometry”). More specifically, in algebra, a linear equation is one that contains simply the variable, which makes them one of the simplest types of equations. For example, a linear equation in one variable has one unknown (the variable) represented by a letter; this letter, usually x, is always to the power of 1, meaning there is no x2 or x3 in the equation.
For instance, x + 3 = 9 is a simple linear equation. To solve such an equation, one must either add, subtract, multiply, and/or divide both sides of the equation by numbers and variables—and do this in the correct order—to end up with a solution: a single variable and single number on opposite sides of the equals sign. In this case, the solution to the linear equation is x = 6.
Finally, linear equations can be further broken down. For example, in the linear equation ax + by + cz + dw = h, in which a, b, c, and d are known numbers and x, y, z, and w are unknown numbers, if h = 0, the linear equation is said to be homogeneous.