 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that, solve the system of linear equations graphically and the equations are y is equal to 4x plus 2 and y is equal to 4x minus 6. Now we know that if the lines intersect that is if we have two lines L1 and L2 which are intersecting lines then there exists a unique solution and if the lines are parallel that is if we have two lines L1 and L2 that are parallel to each other then there exists no solution and if the lines coincide that is there are two lines L1 and L2 that are coinciding then there exist infinitely many solutions. With this key idea let us proceed to the solution. Here we are given this system of equations that is y is equal to 4x plus 2 and y is equal to 4x minus 6. First we graph the two equations and we can use any method of graphing linear equation and in this question we are going to use x and y intercepts to graph these linear equations. Now our first equation is y is equal to 4x plus 2 and we will use x and y intercept to draw the lines graphically. Now to find y and x intercepts we will subsequently put the values of x and y as 0. Now to find y intercept we will put the value of x as 0 in this equation and we get y is equal to 4 into 0 plus 2 which implies that y is equal to 0 plus 2 which is equal to 2. So we say that the y intercept is given by the coordinates 0 to. Now to find x intercept we will put the value of y as 0 in this equation and we get 0 is equal to 4 into x plus 2 that is 4x plus 2 which implies that 4x is equal to minus of 2 that is x is given by minus 2 by 4 which is equal to minus 1 by 2. So the x intercept is given by the coordinates minus 1 by 2 0. Now we have got the value of the y intercept and the x intercept and now we shall plot these points on the coordinate plane and now we draw the axis. This is the horizontal axis that is x axis and here is the vertical axis that is y axis and now we shall plot the point 0 2 on the coordinate plane and here we will take 0 on x axis and 2 on y axis and we put a dot here and this is the point with the coordinates 0 2 and now we shall plot the point minus 1 by 2 0 on the coordinate plane minus of 1 by 2 is equal to minus of 0.5. So we shall take minus of 0.5 on x axis and 0 on y axis and here we get the required point with the coordinates minus of 1 by 2 0. Now we join these two points with our scale and then we extend this line and this is the required graph for the equation y is equal to 4x plus 2 and now we graph the line y is equal to 4x minus 6 and here also to find x intercept we put the value of y as 0 in this equation that is for y is equal to 0 the equation becomes 0 is equal to 4x minus 6 which implies that 4x is equal to 6 that is x is equal to 6 by 4 which is equal to 3 by 2 and is equal to 1.5 therefore x intercept is given by the coordinates 1.50 similarly to find y intercept we will put the value of x as 0 in this equation and we get y is equal to 4 into 0 minus 6 that is y is equal to minus 6 so we say that the y intercept is given by the coordinates 0 minus 6 and now we have got the values of x intercept and y intercept as the points 1.50 and 0 minus 6 and now we shall plot these points and the same coordinate plane now to plot the point 1.50 we shall take 1.5 on x axis and 0 on y axis and we put a dot here and we got this point which has coordinates 1.50 now we shall plot the point 0 minus 6 and for this we take 0 on x axis and minus 6 on y axis and we put a dot here now we join these two points and then extend this line and this is the required graph of the equation y is equal to 4x minus 6 and now we shall find slopes for these two lines and now if we take the first line that is y is equal to 4x plus 2 now to find slope we take two corner points one corner point is this which has coordinates 0 2 and the other corner point we take is this with the coordinates minus 1 minus 2 and now we know that slope is given by the formula that is rise over run so now we shall find the values of rise and run now to find the value of rise we move downwards from the point that was 0 2 and we count the number of squares that was 1 2 3 and 4 and as we move downwards therefore we take negative sign for rise and when we move one unit towards left so as to reach point minus 1 minus 2 so we say that run is given by 1 and as we move towards left therefore we take negative sign for run as well therefore slope for the line y is equal to 4x plus 2 is given by rise over run that is minus 4 by minus 1 which is equal to 4 and similarly for the line y is equal to 4x minus 6 again we take two corner points one point is this which has coordinates 2 2 and the other corner point is given by 1 minus 2 and now we find rise and run for this line now we see that as we are moving from point A to point B we are going for units downwards therefore we say that rise is given by minus 4 and as we are moving from point B to point C we are moving one unit towards left therefore run is given by minus 1 therefore slope for the second line will be equal to rise over run that is minus 4 by minus 1 which is equal to 4 as we see that the two lines have same slope so we can say that these two lines are parallel and from the key idea we know that if the lines are parallel that is if there are two lines m1 and l2 that are parallel to each other then there exists no solution and here as we see that the two lines are parallel therefore there exists no solution so we can say that since the two lines are parallel so there exists no solution which is the required answer this completes our session hope you enjoyed this session