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RD Sharma Solutions for Class 9 Maths Chapter 13: Linear Equations in 2 Variables

An equation having 2 variables can be plotted on a graph representing a straight line called a Linear equation. In this chapter, we will learn how to form a linear equation using 2 variables. For example, let's say a, b and c are real non-zero numbers. Then ax+by+c = 0 can be said as a Linear equation where x and y are variables. This will help the students understand the solutions and use the variables in terms of the equation. For example, If M and N is the number of apples that 2 individuals have, and in total, they have 35 apples. Then by the linear equation, we can say M + N = 35.

In order to solve a linear equation, we've to keep in mind that every linear equation has a unique solution. The process of solving the equations involves determining the value of variables. The value of the variables can be written in ordered pairs such as (5, 9). If we write an equation 2x + 5y = 7. For the sake of simplicity, we can see that the value of the variables is (1, 1). But, if we keep digging more, we can also see that this linear equation has another solution such as (7/2, 0) or (0, 7/5).

Linear equations also have a graphical representation. If we plot several values to the equation, let's say 4x + 9y = 13, on the graph, it will represent this as a straight line. We will also learn about the equations parallel to the X-axis and Y-axis. When one of the variables is zero and the other is non-zero, then the other axis will have some value. We can plot the line parallel to that non-zero axis then.