Difference between LINEAR and NON-LINEAR equations

Once again, we bring you an interesting math lesson, this time about equations. Specifically, we will see what linear equations are and what nonlinear equations are, in order to find their difference. In addition, throughout the lesson we will present examples, so that it is easier to understand and you can perform the exercises that we propose at the end. Here we tell you what is the difference between linear and nonlinear equations with examples, take note!

Index

1. what is an equation
2. What is the difference between linear and nonlinear equations
3. Examples of linear and nonlinear equations
4. Exercise
5. Solution

A equation is, in algebra, that equality in which letters with unknown value appear which we will call unknowns.

Thus, solving an equation is find the value(s) of the unknowns that transform the equation into an identity, that is, that get one part of the equal to give the same number as the other part.

We are going to discover the most outstanding difference between linear and nonlinear equations:

• The Linear equation, also known as simple equation, is one that has one or several unknowns added together, although each unknown can have a coefficient. If we have only one unknown, the result is specifically a number, but if we have two unknowns, the result is a straight line. An example of a linear equation is 3x - 5 = 10.
• The nonlinear equations, unlike the previous ones, They are not first grade. So an example of a nonlinear equation would be 3x² - 5 = 10. Here we include, therefore, both the second degree equations, as well as the cubic, quadratic, sinusoidal...

Another way to quickly differentiate them is through their graphs, since the former are straight, but the latter are not, as can be seen in the image, since they can be parabolas, sets of waves...

We are going to see examples of the difference between linear and non-linear equations and when we can use each of the types of equation for situations in everyday life.

• The linear equations they can be used for when an increase in one variable directly causes an increase or decrease in the other. For example, the weight of a bag of oranges and its price can be related by a linear equation, since if one goes up, the other goes up and vice versa.
• The nonlinear Equations, however, they are often used in science, such as to explain the reproduction of cells in mitosis, a situation in which a non-linear exponential equation would explain it perfectly.

To verify that you have understood what was explained in today's lesson, we advise you to solve the following exercises and check them with the solutions in the later section.

1. Classify the following sentences into true and false.

• A nonlinear equation can be a straight line, as long as it is decreasing.
• A linear equation can have exponent 10.
• A linear equation cannot have two unknowns, since it has to be of degree 1.
• The only way to tell if an equation is linear or nonlinear is by looking at its graph.

2. Tell which of the functions in the image are linear and which are nonlinear.

Now let's check how the resolution of exercises has gone for you.

1. Classify the following sentences into true and false.

• A nonlinear equation can be a straight line, as long as it is decreasing: false, if it is a straight line it will be a linear equation.
• A linear equation can have exponent 10: false, a linear equation always has degree 1.
• A linear equation cannot have two unknowns, since it has to be of degree 1: false, because, although it is true that has to have degree 1 to be a linear equation, that has nothing to do with the number of unknowns, which can to vary.
• The only way to differentiate whether an equation is linear or non-linear is by analyzing its graph: false, we can also differentiate them numerically, based on the degree.

2. Tell which of the functions in the image are linear and which are nonlinear.

Graphically, we can see how the first one is linear, while the others are non-linear, since only the first one is a straight line. However, we can also see it from the numerical function itself, since only the first has degree one.

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