Question

        application of pair of linear equations in two variables in the daily life of people of assam. plse fast response ​

Answer 1

Applications of Linear Systems with Two Variables

LEARNING OBJECTIVES

Set up and solve applications involving relationships between two variables.

Set up and solve mixture problems.

Set up and solve uniform motion problems (distance problems).

Problems Involving Relationships between Two Variables

If we translate an application to a mathematical setup using two variables, then we need to form a linear system with two equations. Setting up word problems with two variables often simplifies the entire process, particularly when the relationships between the variables are not so clear.

Answer 2

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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.