Applications of Linear Equations

A linear equation is an equation where the highest power of the variable is 1. It can involve one variable, two variables, and more. A linear equation combines variables and constants, where the variables have a power of 1. Ax + By = C is the standard form of a linear equation, where a and b are coefficients, x and y are variables, and c is the constant. Linear equations form a straight line if plotted on a graph. The graph of a linear equation is given below:

The applications of linear equations are vast. While solving real-life problems using algebra, we change the given situation into a mathematical statement that clearly explains the relationship between the unknown variables and the information provided. Here are the steps to turn a real-life problem into a mathematical statement. 

• Change the problem statement to a mathematical statement and set it up in the form of an algebraic expression that describes the problem exactly.
• Find the unknown values in the problem and represent them using variables. 
• Read the problems multiple times and mark the data, keywords, and phrases. Organize the information sequentially. 
• Form an equation using the given information and algebraic expressions, then solve it using suitable methods.
• Recheck the solution to your problem statement and analyze whether it suits the criteria of the problem. 

Using these steps and the applications of linear equations, word problems can be solved easily. Linear applications are used in real life to find unknown ages, calculate speed, distance, or time, and solve problems related to force and pressure. 
 

Linear equations are used not only in academics but also in many fields such as finance, engineering, science, and everyday life. By representing real-life situations in mathematical terms, linear equations help to predict outcomes, calculate unknown values, make predictions, and analyze relationships. Below are some of the real-life applications of linear equations. 

• Finance and Budgeting: In finance and budgeting, linear equations are used to calculate expenses, savings, and profits. If a company knows its fixed cost and variable cost per unit, it can find the break-even point by solving a linear equation. 
• Construction and Architecture: Engineers and architects use linear equations to calculate dimensions, costs, and material requirements. For example, if the cost of materials increases in proportion to the area, we can use a linear equation to calculate the total cost. 
• Agriculture and Farming: Farmers use linear equations to predict crop yields based on the fertilizers used, land area, or costs. If every acre of land produces 2 tons of wheat, the total yield Y is Y = 2x, where x is the total acres. 
• Chemistry: In chemistry, linear equations help in mixing solutions of different concentrations to achieve a desired mixture. A chemist can use a linear equation to calculate how much of each solution is needed to get a mixture with a desired concentration. 
• Everyday Problem-Solving: Linear equations are used in everyday problem-solving in situations such as dividing expenses among friends, or calculating taxi fares, which involve linear equations.