Understanding Linear Equations and Inequalities

This video tutorial explains the differences between linear equations and linear inequalities in two variables. It covers how solutions to linear equations form a line on a graph, while solutions to linear inequalities form a half-plane. The video also discusses how to verify solutions using substitution and the significance of solid and dashed boundary lines in inequalities.

What is the main difference between a linear equation and a linear inequality?

• A linear equation forms a half-plane, while a linear inequality forms a line.

• A linear equation has no solutions, while a linear inequality has solutions.

• A linear equation has an equal sign, while a linear inequality has inequality symbols.

• A linear equation has inequality symbols, while a linear inequality has an equal sign.

What do the solutions to a linear equation form when graphed on a coordinate plane?

• A half-plane

• A parabola

• A line

• A circle

Which ordered pair is a solution to the linear equation if it lies on the line?

• Any ordered pair

• An ordered pair not on the line

• An ordered pair in the shaded region

• An ordered pair on the line

What do the solutions to a linear inequality form on a graph?

• A line

• A half-plane

• A circle

• A parabola

When is the boundary line of a linear inequality solid?

• When the inequality symbol is less than

• When the inequality symbol is greater than

• When the inequality symbol is not equal to

• When the inequality symbol includes equal to

What does a dashed boundary line indicate in a linear inequality graph?

• The line represents all solutions

• The line is included in the solution

• The line is not included in the solution

• The line is a solution to the equation

Which ordered pair is a solution to the inequality if it lies in the shaded region?

• An ordered pair outside the shaded region

• An ordered pair in the shaded region

• An ordered pair on the solid line

• An ordered pair on the dashed line

What happens when you substitute an ordered pair into a linear inequality and the result is true?

• The ordered pair is a solution

• The ordered pair is outside the shaded region

• The ordered pair is not a solution

• The ordered pair is on the dashed line

Why is it important to recognize the difference between graphs of linear inequalities?

• To understand the inequality symbol's impact on the graph

• To find the exact solution

• To determine the number of solutions

• To identify the type of line used

What does a solid boundary line in a linear inequality graph indicate?

• The line is dashed

• The line represents no solutions

• The line is part of the solution

• The line is not part of the solution