Solution to system of inequalities

Which graph best represents the solution to the system?
x + y ≤ 6
​x + 2y ≤ 8

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To solve a system of inequalities, graph each inequality.  The coordinates in the overlap of the two inequalities are solutions to the system, since those are the points which satisfy both inequalities.

To graph x + y ≤ 6
- get in slope-intercept form

y ≤ -x + 6   {slope is -1 and y-intercept is 6}

- graph the boundary line, y = -x + 6
- put a point on the y-intercept, 6
- since the slope is -1, go down 1 and to the right 1 and
put another point down
- draw a solid line through the two points, since it
contains the ≤ sign
- shade the area below the line, since it is ≤

To graph x + 2y ≤ 8
- get in slope-intercept form

y ≤ (-1/2)x + 4   {slope is -1/2 and y-intercept is 4}

- graph the boundary line, y = (1/2)x +4
- put a point on the y-intercept, 4
- since the slope is -1/2, go down 1 and to the right 2
and put another point down
- draw a solid line through the two points, since it
contains the ≤ sign
- shade the area below the line, since it is ≤

​The overlap is the solution set to the system of inequalities.

The correct answer is D.

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