Graphing Inequalities

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SAT Math › Graphing Inequalities

Questions 1 - 10
1

Screen shot 2020 09 29 at 12.41.34 pm

If the system of inequalities and is graphed on the xy- plane above, which quadrant contains no solutions to the system?

There are solutions in all 4 quadrants.

II

III

IV

Explanation

The graph of the system of inequalities is shown below. The solution (in purple) is present in all four regions.

Screen shot 2020 09 29 at 12.43.48 pm

2

Screen shot 2020 09 29 at 12.44.36 pm

The graph shown above is best represented by which inequality?

Explanation

The x-intercept is (4,0) so when equals 0, , and the y-intercept is (0,3) so when equals 0, . These points only work for a line corresponding to . To determine which direction the inequality points, you can plug in any point. If we use (0,0), , so this is the direction the inequality must face.

3

For the following system of equations, what shape does the corresponding graph make:

Square

Triangle

Rectangle

It does not form a shape.

Explanation

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.”

Screen shot 2020 09 29 at 10.05.26 am

4

Screen shot 2020 09 29 at 12.38.38 pm

If the system of inequalities and is graphed on the xy- plane above, which quadrant contains no solutions to the system?

II

III

IV

There are solutions in all 4 quadrants.

Explanation

The graph of the system of inequalities is shown below. The solution (in purple) is present in all four regions.

Screen shot 2020 09 29 at 12.40.48 pm

5

Which of the following graphs correctly describes the system of inequalities:

Screen shot 2020 09 29 at 11.43.20 am

Screen shot 2020 09 29 at 11.43.41 am

Screen shot 2020 09 29 at 11.43.45 am

Screen shot 2020 09 29 at 11.43.50 am

Explanation

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.

6

Which of the following are solutions to the system of equations and ?

I)

II)

III)

I

II

I and II

I, II, and III

Explanation

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. does not fulfill . appears to fulfill both conditions but . 18 is not greater than 8, leaving only as a possible solution.

7

For the following system of equations, what shape does the corresponding graph make:

Square

Triangle

Rectangle

It does not form a shape

Explanation

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.”

Screen shot 2020 09 29 at 11.41.58 am

8

Screen shot 2020 09 29 at 11.46.39 am

If the system of inequalities and is graphed on the xy- plane above, which quadrant contains no solutions to the system?

I

II

III

I and II

Explanation

The graph of the system of inequalities is shown below. The solution (in purple) does not go into region I or II.

Screen shot 2020 09 29 at 11.48.13 am

9

Which of the following graphs correctly describes the system of inequalities:

Screen shot 2020 09 29 at 10.10.52 am

Screen shot 2020 09 29 at 10.11.35 am

Screen shot 2020 09 29 at 10.12.10 am

Screen shot 2020 09 29 at 10.12.36 am

Explanation

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.

10

Which of the following ordered pairs (x,y) is a solution to the system of inequalities:

Explanation

This is the only coordinate point that fulfills the system of inequalities.

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