Understanding Systems of Linear Equations

The video tutorial explains how to solve systems of linear equations by graphing. It covers graphing two equations on the same coordinate plane, identifying if the system is inconsistent or dependent, and interpreting the results. The tutorial demonstrates graphing the equations in slope-intercept form and concludes that if the lines coincide, the system has infinite solutions. The solution form is expressed as y = -5x + 7, where x is any real number.

What does it mean if a system of linear equations is inconsistent?

• It has two solutions.

• It has an infinite number of solutions.

• It has exactly one solution.

• It has no solutions.

How do you determine the slope from the equation y = mx + b?

• The slope is the value of m.

• The slope is the value of x.

• The slope is the value of b.

• The slope is the value of y.

What is the vertical intercept of the equation y = -5x + 7?

• (7, 0)

• (0, 7)

• (-5, 0)

• (0, -5)

What is the slope of the line represented by the equation y = -5x + 7?

• -7

• -5

• 7

• 5

How can you graph a line using its slope and intercept?

• Plot any two random points.

• Use the y-intercept only.

• Use the x-intercept only.

• Plot the intercept and use the slope to find another point.

What does it mean if two lines on a graph coincide?

• They are parallel and never meet.

• They are the same line with infinite points in common.

• They intersect at exactly one point.

• They have no points in common.

What is the relationship between the two equations y = -5x + 7 and -2y - 10x = -4?

• They intersect at one point.

• They have no points in common.

• They are the same line.

• They are parallel lines.

If a system of equations is dependent, what can be said about its solutions?

• There are no solutions.

• There are infinite solutions.

• There are two solutions.

• There is exactly one solution.

In a dependent system, if x is any real number, what must y equal in the equation y = -5x + 7?

• y = 7x - 5

• y = -7x + 5

• y = -5x + 7

• y = 5x + 7

What is the form of a solution for a dependent system of equations?

• x = 1, y = 1

• x = 7, y = -5

• x = 0, y = 0

• x = any real number, y = -5x + 7