How Linear Equations Simplify Everyday Maths Problems
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 Real-Life Applications of Linear Equations
1. What is an example of a linear equation in real life?
A real-life example of a linear equation is calculating the total cost of purchasing items. For instance, if each notebook costs $10, and you buy $x$ notebooks, then the total cost $C$ can be modeled by the linear equation: $C = 10x$. Linear equations like these help in budgeting, planning, and making informed decisions about spending.
2. What are some activities where people use linear equations in daily life?
Linear equations are used in various daily activities, including:
- Cooking, to adjust ingredient quantities based on the number of servings
- Splitting bills among friends
- Planning travel times and distances
- Budgeting and expense tracking
- Determining salary based on hours worked
3. What are some real life applications of linear inequalities?
In real life, linear inequalities are widely used to set limits or constraints in situations such as:
- Setting a budget cap while shopping (e.g., spending less than $500, written as $x < 500$)
- Defining safe operating ranges for machines (e.g., temperature $T \leq 100^\circ$C)
- Allocating resources without exceeding totals
- Determining if you have enough material to complete a project
4. What are 5 examples of linear equations?
Here are 5 examples of linear equations commonly used in mathematics and daily life:
- $y = 2x + 3$
- $3a - b = 12$
- $5m = 20$
- $4x + 5y = 9$
- $p - 2q + 7 = 0$
5. How are linear equations applied in business and economics?
Linear equations are crucial in business and economics for financial forecasting, profit calculation, and cost analysis. For example, companies use equations such as $P = R - C$, where $P$ represents profit, $R$ is revenue, and $C$ is cost. This helps in predicting outcomes and making strategic business decisions efficiently, utilizing mathematical models aligned with real-world financial scenarios taught at Vedantu.
6. How do students learn to solve linear equations at Vedantu?
At Vedantu, students learn to solve linear equations through interactive online classes, engaging study materials, and practical problem sets. Vedantu's live sessions feature expert math educators who guide students step-by-step using visual aids and real-life examples, ensuring students understand the concepts thoroughly and can apply them confidently in exams and daily life.
7. Can linear equations help in understanding scientific phenomena?
Yes, linear equations are often used in science to describe relationships such as speed and distance ($d = vt$), chemical reactions, and temperature changes. By modeling these linear relationships, students can better understand and predict scientific outcomes. Vedantu emphasizes these practical applications in its curriculum, making abstract concepts more tangible for learners.
8. What skills can you develop by learning to solve linear equations?
Learning to solve linear equations enhances various core skills, including:
- Logical reasoning
- Analytical thinking
- Problem-solving
- Quantitative aptitude
9. How do you model real-world problems using linear equations?
To model real-world problems with linear equations, first identify the variables and constants involved. Then, establish the relationship, often one that shows how one quantity changes with another. For example, if a taxi fare includes a fixed starting charge plus a per kilometer rate, the total fare can be modeled as $F = a + bk$. Vedantu’s expert tutors teach students to translate daily scenarios into linear equations to build strong foundational skills.
