Which graph best represents the solution set for this system of inequalities

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

Which graph best represents the solution set for this system of inequalities

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 ≤

Which graph best represents the solution set for this system of inequalities

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 ≤

Which graph best represents the solution set for this system of inequalities


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

Which graph best represents the solution set for this system of inequalities

The correct answer is D.

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