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​ALGEBRA 1 STATE TEST PRACTICE

Solution to system of inequalities

12/11/2016

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

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 ≤
Picture
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 ≤
Picture

​The overlap is the solution set to the system of inequalities.
Picture
The correct answer is D.

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