Solving Systems by Graphing Techniques

The video tutorial covers lesson 61, focusing on solving systems of linear equations by graphing. It reviews concepts from chapter five, including slope-intercept and standard form equations. The tutorial provides examples of graphing systems to find solutions, discussing one solution, no solution, and infinite solutions. It also reviews graphing equations in standard form, emphasizing the importance of accurate plotting and understanding different types of solutions.

What is a system of equations?

• A single linear equation

• Two or more linear equations

• A polynomial equation

• A quadratic equation

What does it mean for an ordered pair to be a solution to a system of equations?

• It makes only one of the equations true

• It makes all the equations in the system true

• It makes none of the equations true

• It makes the equations false

In the example y = x + 2 and y = 3x - 2, where do the lines intersect?

• (1, -1)

• (0, 2)

• (2, 1)

• (1, 2)

What is the slope of the line y = 3x - 2?

• 3

• -2

• 1

• 2

What type of solution do parallel lines have?

• Two solutions

• Infinitely many solutions

• No solution

• One solution

What does it mean if two lines have the same slope and the same y-intercept?

• They are parallel

• They intersect at one point

• They have no solution

• They have infinitely many solutions

If two lines overlap completely, what type of solution do they have?

• One solution

• No solution

• Infinitely many solutions

• Two solutions

What should you do if your two lines do not appear to cross at a clear point?

• Assume they do not intersect

• Recheck your graphing

• Ignore the problem

• Change the equations

How do you graph a system of equations in standard form?

• None of the above

• Plot the y-intercept and use the slope

• Convert to slope-intercept form first

• Use the x and y intercepts

What is the x-intercept of the equation 3x + y = -3?

• (0, -3)

• (3, 0)

• (-1, 0)

• (0, 3)