Valid Solutions for Linear Equations

The video tutorial explains a linear equation modeling the purchase of party supplies, where 'x' is the number of boxes of forks and 'y' is the number of boxes of spoons. The tutorial demonstrates how to evaluate ordered pairs to determine if they satisfy the equation, emphasizing the importance of context in real-world problems. It validates solutions and explains why certain pairs do not work, concluding with the correct solutions.

What does the variable x represent in the equation 5x + 6y = 60?

• The number of boxes of spoons purchased

• The total cost of party supplies

• The number of boxes of forks purchased

• The number of party guests

In the context of the equation, what does the number 5 represent?

• The total cost of the party supplies

• The cost of each box of spoons

• The total number of boxes purchased

• The cost of each box of forks

How do you determine if an ordered pair is a viable solution for the equation?

• By checking if the sum of x and y equals 60

• By substituting the values into the equation and checking if the equation holds true

• By ensuring both x and y are positive

• By checking if x is greater than y

Which of the following ordered pairs is a valid solution for the equation 5x + 6y = 60?

• (6, 5)

• (5, 6)

• (10, 0)

• (0, 5)

Why is the ordered pair (12, 0) a valid solution for the equation?

• Because 12 plus 0 equals 60

• Because 5 times 12 plus 6 times 0 equals 60

• Because 6 times 12 equals 60

• Because 5 times 12 equals 60

What is the result of substituting the ordered pair (0, 10) into the equation?

• The result is less than 60

• The equation does not hold true

• The equation holds true

• The result is greater than 60

Why is the ordered pair (5, 6) not a valid solution for the equation?

• Because 5 times 6 plus 6 times 5 equals 60

• Because 5 times 6 plus 6 times 5 equals 61

• Because 5 times 5 plus 6 times 6 equals 60

• Because 5 times 5 plus 6 times 6 equals 61

Why are negative values for x and y not viable in this context?

• Because negative values make the equation invalid

• Because you cannot purchase a negative number of boxes

• Because negative values result in a negative total cost

• Because negative values are not allowed in equations

Which of the following is NOT a valid solution for the equation 5x + 6y = 60?

• (6, 5)

• (12, 0)

• (0, 10)

• (5, 6)

What is the importance of keeping the context of the model in mind when solving the equation?

• To ensure the equation is solved correctly

• To ensure the equation is balanced

• To avoid using negative values which are not realistic

• To make sure the total cost is calculated accurately