Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
Welcome to our Math lesson on Components of Equations, this is the third lesson of our suite of math lessons covering the topic of Variables, Coefficients and Constants. First Order Equations with One Variable, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Like in algebraic expressions, every equation contains variables, coefficients and constants. We have given the meaning of these terms in 6.1. Here, we are going to recall them because of their importance.
Variables are unknown numbers expressed using letters, for example x, y, z, a, b, c, m, n, etc. The ultimate goal when dealing with an equation is to calculate the value of their variables.
Coefficients are numbers that multiply (or divide) variables that precede them. It is normal during calculations for a coefficient to appear after the variable, the equation is rearranged so that all coefficients precede their corresponding variable.
For example, in the equation 3x - 2y = 6, we have two coefficients: 3 and -2 and they are followed by their corresponding variables: namely x and y.
Constants are "free" numbers that are not associated with any variable. They usually appear after the equal sign (giving the value of equation), but we may see constants appearing in the side that contains variables as well, especially in the original form of equations (before making any operation).
For example, in the equation 5x - 2y - 7 = 9, there are two constants: -7 and 9. However, during the solution, they are combined to give a single constant.
Remark! The correct value of the constant is obtained when there is a single number appearing on the same side with variables. If the constant is on the other side of the equation, it must change direction. This process is associated with a change in the constant sign. We will explain why this is so in the last paragraph of this tutorial.
For example, if we have the equation 3x - 2y = 4, the constant is not actually 4 but -4, as we write the equation in the form 3x - 2y - 4 = 0.
In addition, any part of the equation containing the product of a coefficient and one or more variables (they may also be in a certain power) is called a term. Equation terms are separated from each other by 'plus' or 'minus' symbols. This means addition and subtraction act as separators of any equation terms, which on the other hand bear the sign preceding them. The constant also represents a separate term in an equation.
For example, the equation 5x - 2y = 6 contains three terms: 5x; - 2y; and - 6, as we write it as 5x - 2y - 6 = 0.
Find all terms, coefficients and constants in the following equations.
Enjoy the "Components of Equations" math lesson? People who liked the "Variables, Coefficients and Constants. First Order Equations with One Variable lesson found the following resources useful:
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Math tutorial "Variables, Coefficients and Constants. First Order Equations with One Variable" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.