Systems of Linear Inequalities Practice

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the symbol '≥' represent in an inequality?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' represent in an inequality?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

What is the significance of a dotted line when graphing inequalities?

Back

A dotted line indicates that the points on the line are not included in the solution set. This is used for inequalities with '<' or '>'.

Front

What is the significance of a solid line when graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set. This is used for inequalities with '≤' or '≥'.

Front

How do you graph the inequality y < 2x - 1?

Back

First, graph the line y = 2x - 1 using a dotted line. Then, shade the area below the line to represent all points where y is less than 2x - 1.

Front

What is the graphical representation of the inequality y > -2x + 3?

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Graph the line y = -2x + 3 using a dotted line. Then, shade the area above the line to represent all points where y is greater than -2x + 3.

Front

What is the first step in solving a word problem involving linear inequalities?

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The first step is to define the variables that represent the quantities in the problem.

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How can you express a word problem as a system of inequalities?

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Identify the constraints and conditions in the problem, then translate them into mathematical inequalities involving the defined variables.