Question

draw the graph of 2x+y=6 and 2x-y=-2. shade the region bounded by these lines. find the area of the shaded region

Answer 1

Thank you for your question.

First you would have to make a table for the following equations.
Let 2x+y=6 be equation 1.
Let 2x-y=-2 be equation 2.

First, we will take equation 1, suppose some values of x and replace them in equation 1 and get corresponding values for y.

x= -2 -1 0 1 2 
This is the range decided by yourself, if not given in the question for x. 
If I substitute x=-2 in equation 1, I will get the following,

2x+y=6
2(-2)+y=6
-4+y=6
y=2

So we get y=2 for x=-2 for equation 1.

So like this we will complete the table for equation 1 and draw the following table points on the graph.

x= -2 -1 0 1 2
y=  2  4 6 4 2
For equation 2x+y=6 we have following points to draw on the graph.

Similarly we will get the values for equation 2.
x= -2 -1 0 1 2
y= -2  0 2 3 6
For equation 2x-y=-2 we have following points to draw on the graph.

We will shade the region bounded by the lines and find the area of whatever shape is in the making. If its a square, we will get the coordinates of intersecting lines and put them in the square formula to get the answer.

Hope it helps.