This chapter talks about the Pairs of Linear Equations in two Variables and how they can be used to find solutions for real-life problems by solving a given pair of linear equations based on specifically collected data.
It also explains the method to solve a pair of linear equations by graphical representation in the forms of lines, making it easier for the student to understand and grasp. The graphical method is done by finding the points that satisfy the equations and plot them on the graph. Then, connect the points to make the graphs of the respective equations. The final graph will give you the solution of the pair of equations.
The following section explains the methods to solve a system of equations if the intersecting lines are parallel or are coinciding. These methods are essential to understand as they help us solve real-life problems and find numerical applications in the topics that follow and practical issues.
Chapter 3-Pair of Linear Equations in Two Variables also talks about the Algebraic methods to solve a pair of linear equations. Following are the methods discussed in the chapter:
The substitution method includes using the value of any variable in the form of the other variable (for example, if x+y=1, therefore y=1-x) and using this value in the second equation to make it a single variable equation to find the value.
The elimination method involves eliminating one variable from the pair of equations by making the coefficient of the variable the same in both equations. The next step involves adding equations (if signs of the coefficient are opposite) and subtraction (if the signs are the same) to eliminate the variable and obtain the value of the remaining variable.
The cross multiplication method finds its roots in the determinants, and it is one of the fastest methods to work out a solution
The chapter is concluded with a special mention of particular equations which are reducible to a pair of linear equations in two variables. These questions are inevitable for solving real-life problems and have various applications in practical matters.