Solving and Graphing Inequalities in Two Variables

How do you determine if a point is a solution to a linear inequality?

• Graph the point and see if it falls on the line

• Count the number of vowels in the point's coordinates

• Ask a friend if they think the point is a solution

• Substitute the point's coordinates into the inequality and check if it holds true

What is the solution to the system of linear inequalities: y < 2x - 1 and y > -x + 3?

• The solution is the region above the line y = 2x - 1

• The solution is the region to the left of the line y = 2x - 1

• The solution is the region between the two lines y < 2x - 1 and y > -x + 3.

• The solution is the region below the line y = -x + 3

What is the solution to the system of linear inequalities: 2x - y < 4 and x + y > 3?

• The solution is the region where 2x - y > 4 and x + y < 3 intersect.

• The solution is the region where 2x - y < 4 and x + y > 3 intersect.

• The solution is the region where 2x - y = 4 and x + y = 3 intersect.

• The solution is the region where 2x - y < 4 and x + y < 3 intersect.

What is the solution to the system of linear inequalities: 3x - 2y < 6 and 2x + y > 4?

• The solution is a single point on the graph.

• The solution is the region where the two shaded areas do not overlap.

• The solution is a line on the graph.

• The solution is the region where the two shaded areas overlap.

Select the graph for 5x+ y ≤  -1 .

• A

• B

• C

• D

Diagram 2 shows two straight lines on a Cartesian plane. Which of the following regions define linear inequalities

y ≤ x + 5 and y ≥ 2 − x?

• I

• II

• III

• IV

Write the inequality

• y>2/3x-3

• y<2/3x-3

• y≤2/3x-3

• y≥2/3x-3

Write the inequality

• y>-5x-3

• y≥-5x-3

• y<-5x-3

• y≤-5x-3

Write the inequalities

• y≥-2x+3
  y≤x-3

• y>2x+3
  y≥x-3

• y>-2x+3
  y≥x-3

• y<-2x+3
  y≤x-3

When graphing a system of linear inequalities, what does the shaded region represent?

• The solution to the system of inequalities

• The area outside the solution to the system of inequalities

• The area where the lines of the inequalities intersect

• The area where the lines of the inequalities do not intersect