An equation is a statement that says: What is on the left is equal to what is on the right side of the statement. In general case an equation is a statement that has the form A = B, where both A and B are expressions. You will meet several different types:
• An algebraic equations, classified by degree of a variable
• Differential equations
• Integral equations etc.
In this lesson we learn how to deal with linear algebraic equations.
A word linear means that the degree of the variable is equal to one. Beside linear, there are non-linear equations. The non-linear part means that the degree of the variables can be greater or lesser than 1, but can never be equal to 1 (which is reserved for linear equations).
Each equation is made of:
- Variables – the unknown values we are looking for,
- Coefficients – the numbers that multiply the variable,
- Constants or free number(s) – the numbers that do not multiply the variable.
One-step equations can be solved in one step or action. This means we need to perform only one operation, on the left, right or both sides of the equation, to solve the problem.
For example; . To solve the problem, we only need to perform a single subtraction.
Two-step equations can be solved if you perform two operations or actions. All you have to do is to isolate the variable either by using division, multiplication, subtraction, or addition.
Can you imagine an equation that needs two steps to get to the solution? Look at the previous example and ask yourself what could you add to it in order to form a two-step equation? Is a two-step equation? To get the, answer read the lesson about the two-step equations.
Multi-step equations, as the name says, are equations that require more than two steps to find the solution of the problem. You need to perform addition, division, subtraction and/or multiplication several times to solve the problem.
System of equations
Systems of equations can be made of two or more equations. If we are dealing with a system of equations, we need to find the values of each of the variables that solve every equation in the system.
Here is an example of a system of equations:
No matter type of the equation, whether it is one-step or multi-step, you will run into linear or and non-linear equations quite often in life. Fortunately, the principles for solving the equations remain the same, no matter what type they are.