Learn Application of Linear Equation on Vedantu
There are a number of applications of linear equations in Mathematics and in real life. An algebraic expression consists of variables that are equated to each other using an equal “=” sign, it is called an equation. An equation with a degree of one is termed a linear equation. Mathematical knowledge is usually applied through word problems, and the applications of linear equations are observed on a wide scale to solve such word problems. Here is a detailed discussion of the applications of linear equations and how they will fit in the real world.
Linear Equation
A Linear equation is an algebraic expression that consists of variable and equality sign (=). Linear equations are classified based on the number of variables.
Linear Equation with One Variable
The equation which has one degree and one variable is called a linear equation with one variable.
For Example: 5x +30 = 0, 3x + 12 = 48
Linear Equation with Two Variable
The equation which has one and two variables is called a linear equation with two variables.
For Example: 2x + 3y =12, 3x + 7y = 42
Representation of Linear Equations
The graphical representation of the linear equation is ax + by + c = 0. Where a and b are coefficients, x and y are variables, and c is a constant term.
Applications of Linear Equations
The applications of linear equations are vast and are applicable in numerous real-life situations. To handle real-life situations using algebra, we change the given situation into mathematical statements. So that it clearly illustrates the relationship between the unknown variables and the known information. The following are the steps involved to reiterate a situation into a mathematical statement,
Convert the real problem into a mathematical statement and frame it in the form of an algebraic expression that clearly defines the problem situation.
Identify the unknowns in the situation and assign variables of these unknown quantities.
Read the situation clearly a number of times and cite the data, phrases, and keywords. Sequentially organize the obtained information.
Write an equation using the algebraic expression and the provided data in the statement and solve it using systematic equation solving techniques
Reframe the solution to the problem statement and analyze if it exactly suits the problem.
Using these steps, the applications of word problems can be solved easily.
Applications of Linear Equations in Real life
The following are some of the examples in which applications of linear equations are used in real life.
It can be used to solve age related problems.
It is used to calculate speed, distance and time of a moving object.
Geometry related problems can be solved.
It is used to calculate money and percentage related problems.
Work, time and wages problems can be solved.
Problems based on force and pressure can be solved.
FAQs on Application of Linear Equations
1. How can we Calculate the Slope of a Line using Linear Equations?
The equation for the slope of a line is y = mx + c. here, x and y are the variables, c is the constant term, and “m” is the slope of the line. Using trial and error methods, we can find solutions for x and y points and then we will have only one unknown in our equation which is “m”, and we can find that by substituting the x and y values.
2. What is the Elimination Method of Solving Linear equations and When can it be used?
The elimination method of solving linear equations can be used when solving a system of two linear equations which have more than one variable.
This process involves the multiplication of one equation by a constant and then adding or subtracting the equations in order to get an equation in one variable. This can then be solved by the substitution of values to get the final solution. For problems with this kind of situation elimination of solving linear equations is used.
3. What is a linear equation? How is it classified?
A Linear equation is an algebraic expression that consists of variable and equality sign (=). The graphical representation of the linear equation is ax + by + c = 0. Where a and b are coefficients, x and y are variables, and c is a constant term.
Linear equations are classified based on the number of variables.
The equation which has one degree and one variable is called a linear equation with one variable.
For Example: 5x +30 = 0, 3x + 12 = 48
The equation which has one and two variables is called a linear equation with two variables.
For Example: 2x + 3y =12, 3x + 7y = 42
4. What are the real life applications of linear equations?
The following are some of the examples in which applications of linear equations are used in real life.
It can be used to calculate the age of a person in the past, present, and future.
It is used to calculate the speed, distance, and time of a moving object.
It can be used to solve geometrical problems such as lines, parabolas, etc.
It is used to calculate money and percentage-related problems.
Work, time, and wages problems can be solved.
Problems based on the force and pressure of a pipe can be solved.
5. What are the steps to be considered while converting real life problems into linear equations?
Convert the real problem into a mathematical statement and frame it in the form of an algebraic expression that clearly defines the problem situation.
Identify the unknowns in the situation and assign variables of these unknown quantities.
Read the situation clearly a number of times and cite the data, phrases, and keywords. Sequentially organize the obtained information.
Write an equation using the algebraic expression and the provided data in the statement and solve it using systematic equation solving techniques
Reframe the solution to the problem statement and analyze if it exactly suits the problem.
6. How to calculate the slope of a line using linear equations?
The equation for the slope of a line is represented as y = mx + c. here, x and y are the variables, c is the constant term, and “m” is the slope of the line. Using the trial and error methods, we can find solutions for x and y points, and then we will have only one unknown in our equation which is “m”, and we can find that by substituting the x and y values.
