When solving equations, it is important to be systematic in your approach. The steps that follow will help you solve equations systematically. But we don’t have to worry about those difficult equations. In this article, we will learn the fundamental concepts of every equation known to humanity. We will study what an equation is and how many types of equations are there in this world and how solving equations can be easy.
Equations Definition
The equation is very easy to see. Wherever you see two algebraic expressions to the left and right of the equal sign ‘=’, you’ve found an equation. The next section of this article will explain the difference between equations and formulas. First, look at these examples:
Example 1: Is x + y = 13 an equation?
Answer: Yes. x + y = 13 is an equation because there is an equal sign between x + y and 13.
Example 2: Is a – 24 + 13y an equation?
Solution: No! a – 24 + 13y is not an equation because there is no equal sign.
Example 3: Is 66 – 12 = 34 – 3 an equation?
Solution: This is indeed an equation since between 66 – 12 and 34 – 3 are equal. The
equation is used in mathematics to solve for the value of an unknown quantity. They are used to solve many everyday problems including language problems, time and distance, work, profit and loss, and more. Now let’s learn the basic difference between an equation and a formula.
Equation Vs. Expression
Equations and formulas are two different things. Students often confuse the two and make many mistakes. See the table below to clarify the difference between equations and formulas.
equation formula
In mathematics, an equation is formed when two expressions have the same value and are put together with an “equal sign” in the middle. For example: 7x – 2a = 34, 4a + 22 = 3c + b, etc. For example: 34x – 3z + 2y, a + 3k, etc.
Parts of an Equation
In any equation, the left side must equal the right side. Both sides must be the same. Coefficients, variables, operators, constants, terms, expressions, and the ‘=’ symbol are important parts of equations. An equation can contain some or all of these terms centered around the ‘=’ symbol. Let’s study these terms one by one:
Terms: Numerical or algebraic entities that exist around operators are called terms.
Variables: All alphabetic terms in equations whose values are unknown are called variables. Coefficient: The constant term immediately preceding the variable is the coefficient.
Operators: Arithmetic operators such as addition signs, subtraction signs, and equal signs are called operators. An equation can contain only numeric terms, algebraic terms, or both. You will learn how to solve equations in the next module.
How to Solve an Equation?
You can think of the equation as a pair of scales. Both sides of the equation sum to the same value, keeping the scales balanced. Adding or subtracting the same amount on both sides of the equation also applies.
To understand this concept, let’s take an example.
Consider the formula x + 3y = 2a + b. This is a balanced equation. Let’s say we want to add 20 to the left side. The left-hand changes to x + 3y + 20. We need to add 20 on the right side for balance. So the new formula is x + 3y + 20 = 2a + b + 20.
Types of Equation
Equations are classified based on the order of the variables. Order means the power assigned to the variable. A variable of degree 1 is called a linear variable. Similarly, a variable of order 2 is called a secondary variable, and a variable of order3 is called a cubic variable. Equations are classified as linear, quadratic, cubic, and so on. Let’s stake a closer look at them.
Key Notes on Equations
• The solutions or roots of an equation refer to the values of the variables that make the equation true.
If you add, subtract, multiply, or divide the same number into both sides of the equation, the solution remains the same.
• The line represents his linear equation in one or two variables and the parabola represents the quadratic equation.
so, that’s how you can solve equations easily and fast without any fear.
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