Identifying Solutions in Linear Inequalities

What is the first step in determining if an ordered pair is a solution to a system of linear inequalities?

• Graph the inequalities

• Substitute the ordered pair into each inequality

• Check if the ordered pair is in the shaded region

• Find the intersection of the lines

In Example A, what is the result of substituting x = 0 into the inequality x ≤ 3?

• 0 < 3, which is true

• 0 ≤ 3, which is false

• 0 ≤ 3, which is true

• 0 < 3, which is false

In Example A, what is the result of substituting y = 2 and x = 0 into the inequality y > x + 1?

• 2 ≥ 1, which is true

• 2 > 1, which is false

• 2 > 1, which is true

• 2 ≥ 1, which is false

In Example B, why is the ordered pair (-1, -4) not a solution to the system?

• Because -1 is greater than 3

• Because -4 is greater than 0

• Because -4 is not greater than -1 + 1

• Because -1 is not less than or equal to 3

What tool is recommended for graphing systems of linear inequalities?

• Graphing calculator

• Desmos

• Microsoft Excel

• Google Sheets

In Desmos, what indicates the solution to a system of linear inequalities?

• The area where the lines are solid

• The intersection of the lines

• The area where the lines are dashed

• The area where the shaded regions overlap

In the Desmos example, why is the point (3, 2) a solution to the system?

• Because it is in the green shaded area

• Because it is in the red shaded area

• Because it is in the area where the shaded regions overlap

• Because it lies on one of the lines

In the second Desmos example, why is the point (2, -2) not a solution to the system?

• Because it is only in the red shaded area

• Because it is only in the green shaded area

• Because it is outside the shaded regions

• Because it lies on one of the lines

What must you include when entering an ordered pair in Desmos?

• Brackets and a comma

• Parentheses and a comma

• Braces and a comma

• Quotation marks and a comma

In the final example, why is the point (1, -2) not a solution to the system?

• Because it lies on one of the lines

• Because it is not where the shaded regions overlap

• Because it is only in the green shaded area

• Because it is only in the red shaded area