Understanding Systems of Linear Equations

This video tutorial introduces systems of linear equations, explaining how they consist of multiple equations that can be solved to find where their graphs intersect. It demonstrates how to test if an ordered pair is a solution to a system by substituting values into the equations. The tutorial also covers graphing techniques to find solutions, emphasizing the use of slope-intercept form to plot equations and identify intersection points. The video concludes with practical examples of solving systems by graphing.

What is a system of linear equations?

• A single equation with multiple variables

• A set of equations that intersect at a point

• An equation with no solution

• A graph with no lines

How can you verify if an ordered pair is a solution to a system of equations?

• By checking if the pair lies on the x-axis

• By solving each equation separately

• By substituting the pair into both equations and checking for true statements

• By graphing the pair on a coordinate plane

What does it mean if an ordered pair makes both equations in a system true?

• The pair is a solution to a different system

• The pair is only a solution to one equation

• The pair is not a solution

• The pair is a solution to the system

In the practice problem, why was the ordered pair (2, 1) not a solution?

• It was not a valid ordered pair

• It only satisfied one of the equations

• It was not in the correct format

• It made both equations false

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

• Find the y-intercept of each equation

• Convert the equations to slope-intercept form

• Plot random points on the graph

• Solve the equations algebraically

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

• The slope is the constant term

• The slope is the sum of x and y

• The slope is the coefficient of x

• The slope is the y-intercept

What is the significance of the intersection point of two lines on a graph?

• It represents the y-intercept

• It is the x-intercept

• It is the solution to the system of equations

• It is the midpoint of the lines

When graphing, what does the slope of -2 indicate?

• The line rises 2 units for every 1 unit it runs

• The line falls 2 units for every 1 unit it runs

• The line is horizontal

• The line is vertical

What is the y-intercept in the equation y = x + 5?

• 0

• -5

• 1

• 5

How do you write the solution of a system of equations?

• As a list of numbers

• As an ordered pair

• As a fraction

• As a single number