 Hello and welcome to the session. The given question says draw the graphs of the following equations. The given equations are 3x-4y plus x is equal to 0 and the other equation is 3x plus y minus minus equal to 0. Also determine the coordinates of the vertices of the triangle formed by these lines and the x-axis. Let's start with the solution. Well, the given equations are first is 3x minus 4y plus 6 is equal to 0 and the other is 3x plus y minus 9 is equal to 0. Let this be equation number 2. Now first we shall be plotting the graphs and for that we need the points which satisfies both these equations. Starting with the first one this implies that 3x is equal to 4y minus 6 or we have x is equal to 4y minus 6 divided by 3. Let us make a table in which we shall be writing the values of x and y with satisfy equation number 1. Now when we take y is equal to 0 then x is equal to minus 6 divided by 3 which is equal to minus 2. When we take y is equal to 2 here then we have 4 to the 8 and 8 minus 6 is 2 then we have 2 by 3 as the value of x. And when we take y is equal to 3 we have 4, 3 is a 12, 12 minus 6 gives 6 divided by 3 which is equal to 2. So these are the points which satisfy first equation. Now let us find the points that satisfy equation number 2. So this implies that 3x is equal to minus y plus 9 or x is equal to minus y plus 9 divided by 3. Now here also let us make a table of the values of x and y. Now when y is equal to 0 then x is equal to 3 when y is equal to minus 3. So this implies minus into minus is plus 3 plus 9 gives 12 and 12 divided by 3 is 4. So when y is minus 3 x is 4 and then we take y is equal to 3 then we have the numerator as 6 and 6 divided by 3 gives 2. So then y is 3 x is equal to 2. Now let us draw the graphs of both these equations one by one. Now let us plot these points in this graph where this line denotes the x axis where this is the positive x axis and this denotes the from here to this side negative x axis. This is y axis and this is y dash. Now the first point is minus 2 0 that is when x is minus 2 y is 0. So this is the point which denotes minus 2 0. Then we have 2 by 3 and 2 that is when x is 2 by 3 y is equal to 2. So this point is y2 and 2 by 3 is equal to 0.666 so which lies somewhere here. So this is the point which denotes 2 by 3 comma 2. Then we have when x is 2 y is equal to 3 so when x is 2 y is equal to 3 is this point. Now let us join these three points to get the graph of first equation. So let us join these three points. So this is the graph of the first equation which has 3 x minus 4 y plus 6 is equal to 0. Now let us plot these points first as 3 0 which is this point. Then we have 4 minus 3 that is when x is equal to 4 then y is minus 3 which is this point and when x is equal to 2 then y is equal to 3 which is this point which coincides with the point which lies on the first graph. Now joining these three points to get the graph of first equation we have this line which represents 3 x plus y minus 9 is equal to 0. Now according to the question we have to determine the coordinates of the vertices of the triangle formed by these lines and the x-axis. So this is the x-axis and these two are the lines so the point of intersection of these two lines is this point let us denote this by a. The point of intersection of the first line with the x-axis is the point minus 2 0 let us denote this by b and the point of intersection of x-axis with the second line which is 3 x plus y minus 9 is equal to 0 is this point denoting it by c. So here this is the required triangle hence our answer is the vertices of the triangle A, B, C are A's coordinates are 2, 3, B with coordinates minus 2, 0 and C with coordinates 3, 0. So this completes the session bye and take care.