Understanding Dependent Systems in Linear Equations

The video tutorial explains how to solve a system of equations using the elimination method. It demonstrates that the given system is dependent, meaning both equations represent the same line, leading to infinite solutions. The tutorial also covers how to identify dependent systems and graphically represent them. It concludes by discussing different types of systems, including independent and inconsistent systems.

What is the first step in solving the given system of equations using elimination?

• Multiply the first equation by 3.

• Subtract the second equation from the first.

• Add the equations directly.

• Divide the first equation by 2.

Why do we multiply the first equation by 3 in the elimination method?

• To simplify the equation.

• To make the coefficients of y equal.

• To make the coefficients of x equal.

• To eliminate the x variable.

What does the result 0=0 indicate about the system of equations?

• The system has no solution.

• The system has a unique solution.

• The system is dependent.

• The system is inconsistent.

What does it mean when two equations are described as a 'dependent system'?

• They are parallel lines.

• They have no solutions.

• They have exactly one solution.

• They are the same line.

How can you graphically identify a dependent system?

• The lines form a right angle.

• The lines overlap completely.

• The lines are parallel.

• The lines intersect at one point.

What is the slope of the line represented by the equation 2x - y = 14?

• 1

• 2

• -1

• -2

What is the y-intercept of the line 2x - y = 14?

• -14

• 0

• 14

• 2

Which of the following describes an inconsistent system?

• The lines are the same.

• The lines form a triangle.

• The lines are parallel and never intersect.

• The lines intersect at one point.

What is a characteristic of an independent system?

• The lines are parallel.

• The lines are the same.

• The lines intersect at exactly one point.

• The lines do not intersect.

In a dependent system, any solution to one equation is also a solution to the other because:

• The equations are identical.

• The equations are unrelated.

• The equations have different slopes.

• The equations are inconsistent.