Final answer:
For certain values of the unknown, if an equation reduces to the same number on both sides, it is classified as independent because it reflects a unique solution to the equation.
Step-by-step explanation:
When both sides of an equation reduce to the same number for certain values of the unknown, the equation is said to be independent. In mathematical terms, this means that the equation holds true for the given values and has a specific solution. This situation often arises in the context of linear equations, which are equations where the unknown number is not raised to any power other than one.
Taking an example from linear equations, if you have two lines with different slopes, then they are independent of each other and will intersect at one unique point, satisfying both equations simultaneously. If these values are substituted into the original equations and both sides reduce to the same number, then you have confirmed that the equations are independent for those values.