Exploring Systems of Equations through Graphing

This video tutorial explains how to solve systems of equations by graphing. It covers the definition of systems of equations, the different types of solutions, and provides step-by-step examples of graphing systems in slope-intercept form and non-slope-intercept form. Special cases are also discussed, with emphasis on identifying solutions where lines intersect.

What is a system of equations?

• Equations that do not intersect

• A single equation with multiple solutions

• Two or more equations that have the same solution

• Two or more equations with different solutions

Which term describes a system with one solution?

• Dependent

• Consistent independent

• Consistent dependent

• Inconsistent

What is the first step in graphing a system of equations?

• Calculate the slope

• Determine if the equations are in slope-intercept form

• Find the x-intercept

• Plot the y-intercept

In the equation y = mx + b, what does 'm' represent?

• The constant term

• The y-intercept

• The slope

• The x-intercept

What is the solution to the system where the lines intersect at (3, -2)?

• (2, -1)

• (1, -3)

• (3, -2)

• (0, 3)

How do you handle a negative sign in front of y when converting to slope-intercept form?

• Multiply by -1

• Ignore it

• Add it to both sides

• Divide by -1

What is the slope of the line given by the equation y = 7x - 3?

• 7

• -3

• 0

• 1

In the second example, what is the y-intercept of the line y = x - 3?

• (0, 3)

• (0, -3)

• (3, 0)

• (-3, 0)

What does it mean if a line does not touch the x-axis?

• It is a vertical line

• It has an undefined slope

• It is a horizontal line

• It has no slope

What is the solution to the system where the lines intersect at (2, -1)?

• (3, -2)

• (2, -1)

• (1, -3)

• (0, -3)