Understanding Solutions to Linear Equations

The video tutorial explains how to determine if an ordered pair is a solution to a linear equation using two methods: graphing and substitution. The graphical method involves plotting the point and checking if it lies on the line, while the substitution method involves replacing variables in the equation with the values from the ordered pair to see if the equation holds true. Examples are provided to illustrate both methods, and the video concludes with a graphical verification of the solutions.

What are the two methods to determine if an ordered pair is a solution to a linear equation?

• Substitution and division

• Elimination and substitution

• Graphing and substitution

• Graphing and elimination

In the substitution method, what do you do with the values of x and y from the ordered pair?

• Add them to the equation

• Multiply them by the equation

• Substitute them into the equation

• Divide them by the equation

What was the result of substituting the ordered pair (-3, 7) into the equation?

• The equation was incomplete

• The equation was undefined

• The equation was false

• The equation was true

What does it mean if a point is not on the line when graphing a linear equation?

• The ordered pair is a solution

• The ordered pair is not a solution

• The ordered pair is undefined

• The ordered pair is incorrect

What was the result of substituting the ordered pair (3, -7) into the equation?

• The equation was incomplete

• The equation was undefined

• The equation was false

• The equation was true

What is the result of substituting the ordered pair (5, -12) into the equation?

• The equation was incomplete

• The equation was undefined

• The equation was false

• The equation was true

What does it mean if a point is on the line when graphing a linear equation?

• The ordered pair is incorrect

• The ordered pair is undefined

• The ordered pair is a solution

• The ordered pair is not a solution

How many solutions does a linear equation in two variables have?

• One solution

• Two solutions

• No solutions

• Infinite solutions

What is the graphical representation of a linear equation?

• A point

• A line

• A circle

• A curve

What is the form of an ordered pair?

• y - x

• x, y

• x + y

• y, x