If you don't have a graphing calculator the easiest way to do this is to put these in slope intercept form y=mx+b
In order to do this, solve for y
x+y=4
subtract x
y=-x+4
x-y=2
subtract x
-y=-x+2
Multiply by -1
y=x-2
Now you have two equations in slope intercept form
y=-x+4
y=x-2
To graph these, start with the y intercepts as your beginning point. We know the y-intercepts because the equations are in slope intercept form y=mx+b where b is the y intercept. So our two points are
(0,4) and (0,-2)
Then you can use the slope or the M value in the equation to get the other points.
for the first equation, we can use the slope of -1 and go down one and one to the left on the graph to get the point (-1,3) do this again to get (-2,2)
The same thing can be done with the second equation on the slope is positive 1
so we go up and to the right to (1,-1), (0,0)
Here is what the graph looks like
the solution is where the lines cross, you will have a value for x and a value for y