 Hello and welcome to the session. In this session, we will discuss the following question and the question says solve graphically the equations x plus 2y is equal to 4, 3x plus 2y is equal to 6. Let's start the solution now. We are given the two equations x plus 2y is equal to 4 and 3x plus 2y is equal to 6 and we have to solve them graphically. For this step one is draw the graphs of the two equations on the same coordinate plane. Now to draw the graph of the first equation that is x plus 2y is equal to 4. We will first make the table of values for the equation x plus 2y is equal to 4. To make the table of values, we now substitute values of y and obtain values of x. Now the given equation is x plus 2y is equal to 4. This implies x is equal to 4 minus 2y. So we have expressed the variable x in terms of the variable y. Now we substitute different values of y and obtain values of x. So for y is equal to 0, we get x is equal to 4 minus 2 into 0 which implies x is equal to 4. Now for y is equal to 1, we get x is equal to 4 minus 2 into 1 which implies x is equal to 4 minus 2 which is equal to 2 and for y is equal to 2, we get x is equal to 4 minus 2 into 2 which implies x is equal to 0. We will now put the values of x and y that we have just obtained in this table of values. For y is equal to 0, we got x is equal to 4. So we write these values here. Also for y is equal to 1, we have x is equal to 2 and for y is equal to 2, x is equal to 0 that is y is 2 and x is 0. So we have obtained three ordered pairs in this way. Now we will plot the points ordered pair for 0, ordered pair 2 1 and ordered pair 0 2. So this is the coordinate plane and we have made two axes on this coordinate plane. The horizontal axis is the x axis and the vertical axis is y axis. We will now plot these three points on the coordinate plane. We will plot the point ordered pair for 0. Now in the ordered pair for 0, the x coordinate is 4 and y coordinate is 0. So this point for on x axis is the ordered pair for 0 since it has x coordinate equal to 4 and y coordinate equal to 0. Now we should plot the second point that is ordered pair 2 1. The ordered pair 2 1 has x coordinate equal to 2 and y coordinate equal to 1. So first we reach the point 2 on x axis and then remove upwards along the y axis. Can we reach the point 1? So this point is the point ordered pair 2 1. The third point is ordered pair 0 2. Ordered pair 0 2 has x coordinate equal to 0 and y coordinate equal to 2. So this point 2 on y axis is the point ordered pair 0 2 since its x coordinate is 0 and y coordinate is 2. In this way we have plotted the three points. Next we will join these points. So now we will join these three points. So this is the line formed by joining the three points and this line is graphed by the equation x plus 2y is equal to 4. We will now make the table of values for the equation 3x plus 2y is equal to 6. Now the given equation is 3x plus 2y is equal to 6. This implies 2y is equal to 6 minus 3x. This implies y is equal to 6 minus 3x divided by 2. We will now substitute the three values of x and get values for y. So for x is equal to 0 y is equal to 6 minus 3 into 0 upon 2 which is equal to 3. Now for x is equal to 1 we get y is equal to 6 minus 3 into 1 upon 2 which is equal to 1.5 and for x is equal to 2 y is equal to 6 minus 3 into 2 upon 2 which is equal to 0. So for different values of x we have obtained corresponding values of y. So we now put the values of x and y that we have just obtained in this table of values. We obtain for x is equal to 0 y is equal to 3 so we write down this in this table for x is equal to 0 y is 3. For x is equal to 1 y is equal to 1.5 and for x is equal to 2 y is equal to 0. So in this way we have made a table of values. Thus we have obtained three ordered pairs. Now we will plot the points ordered pair 0 3, ordered pair 1 1.5 and ordered pair 2 0. Thus we will plot the three points that we obtained from the second equation in the same coordinate plane. The first point that we will plot is the ordered pair 0 3. Now in the ordered pair 0 3 x coordinate is 0 and y coordinate is 3. So we first reach the point 0 on x axis which is the origin and move upwards along the y axis till we reach the point 3. So this point is the point ordered pair 0 3. The next point is ordered pair 1 1.5. Now in the ordered pair 1 1.5 x coordinate is 1 and y coordinate is 1.5. So we first reach the point 1 on x axis and move upwards along y axis till we reach the point 1.5. So this point is the point ordered pair 1 1.5. The third point is ordered pair 2 0. Now this point 2 on x axis is the point ordered pair 2 0 since it has x coordinate as 2 and y coordinate as 0. So this is the point ordered pair 2 0. Now we will join these points. So we have to join these three points that we obtained from the second equation. So this is the straight line that we obtained by joining these three points and this line is the graph for the equation 3x plus 2y is equal to 6. Now step 2 is see the coordinates of the point of intersection. The two lines we can see that the two lines intersect at the point 1 1.5. So at this point x is equal to 1 and y is equal to 1.5 since this point lies on both the lines therefore ordered pair 1 1.5 is the solution to the given equations. So we can say that since the two lines intersect at the point ordered pair 1 1.5 therefore x is equal to 1 and y is equal to 1.5 is the answer to the given question. With this we end our session. Hope you enjoyed the sessions.