Brilio.net - Linear equations are algebraic equations whose variables are powers of one. Linear equations have solutions that can be found using certain methods, such as elimination, substitution, or graphs. Linear equations can have one, two, or more variables.
So in this article, brilio.net will provide examples of linear equations with one variable and the answers. Not only that, there is also a definition of linear equations, their characteristics and steps so that it is easier for you to understand them. In simple terms, a one-variable linear equation is a linear equation that only has one variable, for example x, y, or z.
One-variable linear equations can be solved by moving all the variables to one side and all the constants to the other side, then simplifying and dividing both sides by the variable coefficient.
The following is an example of a one-variable linear equation question and the answer, quoted by brilio.net from various sources, Wednesday (13/3).
Definition of linear equation.
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Linear equations are a form of mathematical equation that has the highest level of power, namely the power of one. In general, linear equations can be written in the form ax + b = c, where a, b, and c are constants, and x is a variable. This equation has the property that when the value of x changes, the other values will also change linearly.
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Linear equations can also be seen in the form of straight lines on the coordinate plane. The line will have a slope and shift according to the constants a, b, and c in the linear equation. When properly understood, linear equations can be used to model many phenomena in everyday life, such as the movement of objects, population growth, or changes in temperature.
In learning mathematics, linear equations are often used as a basis for understanding further mathematical concepts, so it is very important to understand the concept of linear equations in depth. With a good understanding of linear equations, you can easily solve various problems involving linear relationships between variables.
Characteristics of linear equations.
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Characteristics of linear equations include:
1. Only consists of variables x and y.
Linear equations only contain two variables, namely x and y. This is different from quadratic equations or exponential equations which can have more than two variables.
2. The graph forms a straight line.
The graph of a linear equation always forms a straight line when plotted on the Cartesian plane. This is because the variables x and y only have powers of one in the equation, so the graph does not have any curves or curves.
3. Does not contain a variable power higher than one.
Linear equations do not contain variable powers higher than one. For example, there are no x^2 or y^3 variables in a linear equation.
4. Solutions can be found easily.
Due to its simple nature, solutions to linear equations can be found easily using substitution, elimination methods, or using graphs.
Basic steps to solve linear equations.
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Linear equations are mathematical equations consisting of variables expressed in linear form. To solve linear equations, there are several basic steps that need to be followed.
The first step is to simplify the equation by combining similar variables. Then, the second step is to eliminate unnecessary variables by subtracting or adding both sides of the equation. The third step is to find the value of the unknown variable by isolating the variable.
For example, if given the equation 2x + 3 = 11, the first step is to subtract 3 from both sides of the equation, thus getting 2x = 8. Then, the second step is to divide both sides of the equation by 2, so that the value x = 4 is obtained.
By following these basic steps, you can solve linear equations easily. This can also help students understand and solve linear equation problems better.
Examples of linear equation questions and answers that are easy to understand.
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Example question 1
3x + 5 = 20, calculate the results of this linear equation!
Solution:
3x = 20 - 5
3x = 15
x = 15 / 3
x = 5
Example question 2
2y - 4 = 10, calculate the result of the linear equation!
Solution:
2y = 10 + 4
2y = 14
y = 14 / 2
y = 7
Example question 3
4z + 8 = 24, calculate the results of this linear equation!
Solution:
4z = 24 - 8
4z = 16
z = 16 / 4
z = 4
Example question 4
6a - 12 = 30, calculate the result of the linear equation!
Solution:
6a = 30 + 12
6a = 42
a = 42 / 6
a = 7
Example question 5
8b + 16 = 40, calculate the results of this linear equation!
Solution:
8b = 40 - 16
8b = 24
b = 24 / 8
b = 3
Example question 6
5c - 25 = 10, calculate the result of the linear equation!
Solution:
5c = 10 + 25
5c = 35
c = 35 / 5
c = 7