 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that graph the following linear system of equations on graphing calculator and the equations are 3x plus 5y is equal to 5 and 4x minus 6y is equal to 12. Also find their point of intersection. Let us start with the solution of the given question. Here we are given the linear system of equations and the equations are 3x plus 5y is equal to 5 and 4x minus 6y is equal to 12. And we have to graph these equations on graphing calculator and find their point of intersection. First we will enter these equations on graphing calculator for this we write these equations in y is equal to form. Now first equation is 3x plus 5y is equal to 5 and we can write it as 5y is equal to 5 minus 3x which implies that y is equal to 5 upon 5 minus 3 upon 5x that is y is equal to 1 minus 3 upon 5x or it can also be written as y is equal to minus 3 upon 5x plus 1. And the second equation is 4x minus 6y is equal to 12 and we can write it as minus 6y is equal to 12 minus 4x which implies that y is equal to 12 upon minus 6 minus 4 upon minus 6x which further implies that y is equal to minus 2 plus 2 upon 3x or it can also be written as y is equal to 2 by 3x minus 2. Now we have got these two equations in y is equal to form now we shall write these equations on graphing calculator for this first we begin with home screen and press y is equal to key this takes us to the equation entering screen where we will write our equation first let us enter the equation y is equal to minus 3 upon 5x plus 1 into y1 then we add the equation y is equal to 2 upon 3x minus 2 into y2 and we get this display on the screen to view its graph we press graph key on the screen the graph of the linear function y is equal to minus 3 upon 5x plus 1 and the graph of the other linear function 2 by 3x minus 2 will appear we see that both curves are straight lines and now we need to find their point of intersection now if we look at the screen we can clearly see that there is only one point of intersection and we have to find coordinates of this intersecting point to find coordinates of the intersecting point we press second key followed by trace key we will get calculate menu on the screen now see at number five intersect is written so press number five key to know points of intersection we will get the following display now see first curve is written that is y1 is equal to minus 3 upon 5x plus 1 is written so we bring the cursor near the intersecting point on this curve then we press enter key that is this key we get this display now second curve that is y2 is equal to 2 upon 3x minus 2 is displayed so we bring cursor near to the same intersecting point on second curve that is y2 is equal to 2 by 3x minus 2 and again we press enter key now guess appears on screen again we press enter key we get the following display this gives us the coordinates of this point of intersection and it is x is equal to 2.36 and y is equal to minus 0.42 thus the ordered pair 2.36 minus 0.42 is the point of intersection of the given system of equations which is the required answer this completes our session hope you enjoyed this session