SAT Mathematics : Graphing Inequalities
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Example Questions
Example Question #1 : Graphing Inequalities
For the following system of equations, what shape does the corresponding graph make:
Rectangle
Square
It does not form a shape.
Triangle
Triangle
When we graph the three inequalities as equations, we get the below graph. Testing a point within the triangle does in fact fulfill all three conditions, so the shape formed by the inequalities is a triangle. If a tested point within the triangle did not fulfill one or more conditions, then we would have chosen “it does not form a shape.”
Example Question #1 : Graphing Inequalities
Which of the following graphs correctly describes the system of inequalities:
After plotting the lines, shade the regions corresponding to each individual inequality. The area of intersection (in purple) is the solution to the system of inequalities. Another way to check your answer is to pick a point in all four regions delineated by the two equations and test those four coordinate points in the system of inequalities.
Example Question #2 : Graphing Inequalities
For the following system of equations, what shape does the corresponding graph make:
Square
It does not form a shape
Rectangle
Triangle
Triangle
When we graph the three inequalities as equations, we get the below graph. Testing a point within the triangle does in fact fulfill all three conditions, so the shape formed by the inequalities is a triangle. If a tested point within the triangle did not fulfill one or more conditions, then we would have chosen “it does not form a shape.”
Example Question #3 : Graphing Inequalities
Which of the following graphs correctly describes the system of inequalities:
After plotting the lines, shade the regions corresponding to each individual inequality. The area of intersection (in purple) is the solution to the system of inequalities. Another way to check your answer is to pick a point in all four regions delineated by the two equations and test those four coordinate points in the system of inequalities.
Example Question #3 : Graphing Inequalities
Which of the following ordered pairs (x,y) is a solution to the system of inequalities:
This is the only coordinate point that fulfills the system of inequalities.
Example Question #4 : Graphing Inequalities
If the system of inequalities 
I and II
II
III
I
I and II
The graph of the system of inequalities is shown below. The solution (in purple) does not go into region I or II.
Example Question #5 : Graphing Inequalities
If the system of inequalities 
There are solutions in all 4 quadrants.
IV
II
III
There are solutions in all 4 quadrants.
The graph of the system of inequalities is shown below. The solution (in purple) is present in all four regions.
Example Question #6 : Graphing Inequalities
If the system of inequalities 
There are solutions in all 4 quadrants.
II
IV
III
There are solutions in all 4 quadrants.
The graph of the system of inequalities is shown below. The solution (in purple) is present in all four regions.
Example Question #8 : Graphing Inequalities
The graph shown above is best represented by which inequality?
The x-intercept is (4,0) so when 
Example Question #8 : Graphing Inequalities
Which of the following are solutions to the system of equations 
I)
II)
III)
I and II
I, II, and III
I
II
I
With this question, it is important to recognize the system of inequalities utilizes the “greater than” sign, not the “greater than or equal to” sign. 
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