A linear equation is any equation involving one or two variables whose exponents are one. In the case of one variable, one solution exists for the equation. For example, with 2_x_ = 6, x can only be 3.
One obvious difference between linear equations and inequalities is the solution set. A linear equation of two variables can have more than one solution.
For instance, with x = 2_y_ + 3, (5, 1), then (3, 0) and (1, -1) are all solutions to the equation.
In each pair, x is the first value and y is the second value. However, these solutions fall on the exact line described by y = ½ x – 3/2.
If the inequality were x ? 2_y_ + 3, the same linear solutions just given would exist in addition to (3, -1), (3, -2) and (3, -3), where multiple solutions can exist for the same value of x or the same value of y only for inequalities. The "?" means that it is unknown whether x is greater than or less than 2_y_ + 3. The first number in each pair is the x value and the second is the y value.
