 Hello and welcome to the session. Today I'll help you with the following question. The question says, is the following pair of linear equations consistent or inconsistent? If consistent, obtain the solution graphically. 2x plus y minus x equal to 0 and 4x minus 2y minus 4 equal to 0. Let's discuss the key idea for this question. Now if a pair of linear equations is given by a1x plus b1y plus c1 equal to 0 and a2x plus b2y plus c2 equal to 0, then if a1 upon a2 is not equal to b1 upon b2, then this implies that the pair of linear equations is consistent. And if a1 upon a2 is equal to b1 upon b2 and not equal to c1 upon c2, then this implies that the pair of linear equations is inconsistent. Also, if a1 upon a2 is equal to b1 upon b2 is equal to c1 upon c2, then this implies that the pair of linear equations is dependent and consistent. Now let's move on to the solution. The given pair of equations is 2x plus y minus 6 equal to 0 and 4x minus 2y minus 4 equal to 0. Here we have a1 is equal to 2, b1 is equal to 1 and c1 is equal to minus 6. Also a2 is equal to 4, b2 is equal to minus 2 and c2 is equal to minus 4. Consider a1 upon a2 and this is equal to 2 upon 4 equal to 1 upon 2, then b1 upon b2 is equal to 1 upon minus 2 that is equal to minus 1 upon 2. Now from these two conditions we say that a1 upon a2 is not equal to b1 upon b2, hence from the key idea we say that the given pair of linear equations is consistent. Now we should obtain the solution of the given pair of linear equations graphically. This is equation 1 and this is equation 2. Now we will draw the graphs of equation 1 and equation 2. For this we find two solutions of each of these equations. If we take x as 0 in this equation then we get y as 6 and if we take x as 1 in this equation then the value of y is 4. In this equation if we take x as 0 we get y as minus 2 and if x is taken as 1 then value of y is 0. So we have got the solutions for each of these equations. Now we shall draw the graph of these equations. First point that we have to plot is the point a which coordinates 0,6 for this equation. This is the point which represents the point a which coordinates 0,6. Next we have the point b which coordinates 1,4. This point represents b which coordinates 1,4. Now we shall join both these points. We have got a straight line and joining the points a and b. This straight line represents the equation 2x plus y minus 6 equal to 0. Next we have the solution for this equation. Let's name this point as c which coordinates 0, minus 2. This point represents the point c which coordinates 0, minus 2. Next is the point d which coordinates 1,0. This point represents point d which coordinates 1,0. Now we join these two points. So we have got the straight line and joining the points c and d. This line represents the equation 4x minus 2y minus 4 equal to 0. As you can see these two lines intersect at a point and we know that if the lines intersect at a single point then that pair of equations has a unique solution. So we can say that this pair of equation has a unique solution which is represented by this point which coordinates 2,2. Hence we say the given pair of equations is consistent and its solution is x equal to 2, y equal to 2 that is unique solution. This is the final answer. So hope you enjoyed the session. Have a good day.