 Hi and welcome to the session. Let's work out the following question. The question says, draw a graph of 2x plus y equals to 6 and 2x minus y plus 2 is equal to 0. Shade the region bounded by these lines and x-axis, find the area of the shaded region. Let's start with the solution to this question. First of all we need to find the points lying on this and this line. First we'll consider 2x plus y equals to 6. This implies that y is equal to 6 minus 2x. Now the points lying on this line will be when x is 0, y is 6, when x is 3, y is 0, when x is 1, y is 4. Similarly we find out the points lying on the line 2x minus y plus 2 equal to 0. Now this is the same as y is equal to 2x plus 2. Three points lying on this line will be when x is 0, y is 2, when x is minus 1, y is 0, when x is 1, y is 4. So now we plot these two lines on the graph by plotting the points first of all. So like this we have these two lines and this shaded region is the required region which is bounded by these two lines and the x-axis. So by plotting the points and joining them we see that these two lines intersect at the point 1, 4. That is x is 1, y is 4 is the solution. Also we see that area of the shaded region say a, b, c will be at this be the point a, b, c and let this altitude be ad. So we see that the area will be half of base that is bc into altitude that is ad. So we have this is equal to half of bc into ad. Now from the graph we see that bc is of measure 4 units ad is of measure 4 units. So this is equal to half of 4 into 4 that is equal to 8 square units. So our answer to this question is that area of the shaded region is 8 square units. I hope that you understood the solution and enjoyed the session. Have a good day.