Linear Equation

This class for grade 9

  We learn how to solve linear equation

The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 2 = 0 has only one solution as x = -2

We  learn single variable and two variable equation

Students can solve systems of linear equations by graphing. Students are able to determine if a system of linear equations has no solution, one solution, or infinitely many solutions. Students are able to determine which method is best to solve a system of linear equations.

The main objective of linear programming is to maximize or minimize the numerical value. It consists of linear functions which are subjected to the constraints in the form of linear equations or in the form of inequalities.

Applications of Linear Equations Solved Example

Example:

Rishi is twice as old as Vani. 10 years ago his age was thrice of Vani. Find their present ages.

Solution:

In this word problem, the ages of Rishi and Vani are unknown quantities. Therefore as discussed above, let us first choose variables for the unknowns.

Let us assume that Vani’s present age is ‘x’ years. Since Rishi’s present age is 2 times that of Vani, therefore his present age can be assumed to be ‘2x’.

10 years ago, Vani’s age would have been ‘x – 10 ’, and Rishi’s age would have been ‘2x – 10’. According to the problem statement, 10 years ago, Rishi’s age was thrice of Vani, i.e. 2x – 10 = 3(x – 10).

We have our linear equation in the variable ‘x’ which clearly defines the problem statement. Now we can solve this linear equation easily and get the result.