 Hello and welcome to the session. In this session first we will discuss about linear equations. Any equation which can be put in the form ax plus by plus c equal to 0 where we have ab and c are the real numbers and a is not equal to 0 and v is also not equal to 0 and v is called a linear equation in two variables. So it means that we can think of many, many such equations like for example an equation of the kind 2x plus 3y is equal to 5 is a linear equation in two variables and in this case x and y are the two variables. Next we discuss solution of a linear equation for a linear equation in two variables like ax plus by plus v equal to 0. The solution is written as an ordered pair where the first value is for the variable x and the second value is for the variable y and there is no end to different solutions of a linear equation in two variables. So we say that a linear equation in two variables infinitely many solutions. Let's consider the linear equation 2x plus y equal to 7. As you can see we have two variables x and y in this equation. So this is a linear equation in two variables. Let's try and find out some solutions for this linear equation. Let's take x equal to 0 in this equation. So we get y equal to 7 thus 0 7 is one solution of this linear equation. On taking x equal to 1 in this equation we get y equal to 5. So 1 5 is another solution of the given linear equation. So in this way I am putting different values for x or different values of y we can get the corresponding values for the other variable to get the solution of a given linear equation in two variables. Next we discuss graph of a linear equation in two variables. A linear equation in two variables is represented geometrically by a line whose points make up the collection of solutions of the equation. This is called the graph of a linear equation. So we say to obtain graph of a linear equation in two variables it is enough to plot two points corresponding to two solutions and join them by a line. However we plot more than two such points that we can immediately check the correctness of the graph. Basically the graph of every linear equation in two variables is a straight line. We also say that every point on the graph of a linear equation in two variables is a solution of the linear equation and moreover every solution of the linear equation is a point on the graph of the linear equation and also an equation of the type y equal to mx represents a line passing through the origin. Consider the linear equation 2x minus y plus 3 equal to 0. Let's draw the graph for this linear equation in two variables. To draw the graph we need at least two solutions of the equations. So you can see when we put x equal to 0 in this equation we get y equal to 3 and when we put x equal to 1 in the same equation we get y equal to 5. Now we draw the graph by plotting the two points from this table and we join them by a line. First let's consider the point that coordinates 0, 3. Now here we have x is equal to 0 and y is equal to 3 so this is the required point. Let it be point A that coordinates 0, 3. Now the other point is 1, 5 where we have x is equal to 1 and y is equal to 5 so this is the required point. Let it be point B that coordinates 1, 5. Now we will join these two points by a line. So now this line is 2x minus y plus 3 equal to 0. So this is how we can draw the graph for any given linear equation in two variables. Now we discuss equations of lines parallel to x axis and y axis. We know that x equal to 0 is the equation of y axis and y equal to 0 is the equation of x axis. Then we have graph of the line x equal to a is a straight line parallel to the y axis. Then graph of the line y equal to a is a straight line parallel to the x axis. Let's try and draw the graph of the equation x equal to 5. Now as you know that the graph of x equal to a is a straight line parallel to y axis so in this case also the graph for this line would be a straight line which is parallel to y axis. So this is the line x equal to 5 and it is parallel to the y axis. This completes this session. Hope you have understood the concept of linear equations in two variables.