How to Solve Linear Equations

How to Solve Linear Equations

 In 2022, the JEE Main exam will be conducted in two sessions. As per the latest notification of the exam conducting authority, the JEE Main exam is expected to be conducted in June and July. Proper planning and hard work are necessary for cracking this exam. Students should also gain the speed to solve the problems within the stipulated time. So, mock tests are highly recommended. This will also help the JEE aspirants to experience the real exam scenario.

In mathematics, linear algebra is a topic of great importance and application. It is used in graph theory, determinants, least square approximation etc. As far as the JEE Main exam is concerned, linear equations are a topic of great importance. Students are recommended to learn the previous years’ questions asked for the JEE main exam so that they will be able to understand the exam pattern. 

What is a Linear Equation?

If the highest power of a variable in an equation is 1, then that is a linear equation. An equation of the form px + q = 0 is an example. Here, x is a variable and p, q are real numbers. 

Let us solve an example.

Example: Solve 6x + 9 = 81

Solution:

Given equation is 6x + 9 = 81

We shift the 9 on the LHS to the RHS.

6x = 81 - 9

6x = 72

Divide both sides by 6.

6x/6 = 72/6

=> x = 12

Let us check the value of x by substituting it to the given equation.

6x + 9 = 81

6(12) + 9 = 72 + 9 = 81

The value of x satisfies the given equation. 

Standard form

The standard form of a linear equation having two variables in ax + by + c = 0, where x and y are the variables and a, b, c are real numbers. 

Types of solution

Before solving the equations, it is always recommended to check the type of the solutions. If a1/a2 = b1/b2 = c1/c2, then it is a consistent system of equations and we get infinite solutions. If a1/a2 ≠ b1/b2, then we get a unique solution. If a1/a2 = b1/b2 ≠ c1/c2, then there exists no solution.

Linear programming 

Linear programming deals with maximising or minimising a linear function subject to various constraints. This technique has different applications in guiding quantitative decisions in business planning, in the social and physical sciences, in industrial engineering, etc. A linear programming problem deals with the optimisation problem of two linear variables. The objective function is the function formed using those two linear variables. Constraints, decision variables, non-negative constraints, feasible region, optimisation problems, infeasible region and optimal solution are the important terminologies used in LPP. Linear programming problems are very easy to solve. So, students can easily score marks from linear programming if learnt properly. 

Study materials for the JEE Main exam are available online on different websites. Students are advised to go through revision notes, important formula pdfs, question paper solving videos etc. Visit BYJU’S to learn more about linear programming and solutions from previous years’ questions on linear programming.