Inconsistent systems of equations | Algebra II | Khan Academy

TL;DR

The king's advisor challenges the king and a bird to solve the riddle of the fruit prices, but they discover that the system of equations is inconsistent.

Transcript

The king's advisor, Arbegla, is watching all of this discourse between you, the king, the bird. And he's starting to feel a little bit jealous 'cause he's supposed to be the wise man in the kingdom, the king's closest advisor. So he steps in and says, "okay, so if you and this bird" "are so smart, how about you tackle the Riddle of the Fruit Prices... Read More

Key Insights

• 😉 The king's advisor challenges the king and a bird to solve a riddle involving the cost of apples and bananas.
• 😒 They set up variables and use the given information to create equations representing the total cost of fruits.
• ❓ When attempting to solve the equations using elimination, they find that the system is inconsistent, indicating there is no solution.

Questions & Answers

Q: How does the king's advisor challenge them to solve the riddle of the fruit prices?

The advisor steps in and asks the king and bird to determine the cost of apples and bananas, given the total cost and quantities of fruits bought at different times.

Q: How do the king and bird approach solving the riddle algebraically?

They define variables for the cost of apples (a) and bananas (b) per pound, and use the given information to set up equations representing the total cost of fruits.

Q: What happens when they attempt to solve the system of equations using elimination?

When they multiply one equation by -3 and combine it with the other equation, all the variables cancel out, resulting in the statement 0 = 6, which is not possible.

Q: What conclusion do they reach about the system of equations?

They realize that the system is inconsistent, indicating that either the information provided is incorrect or there was a mistake in accounting or a change in fruit prices.

Summary & Key Takeaways

• The king and a bird are tasked with solving the riddle of the fruit prices, where they need to determine the cost of apples and bananas per pound.

• They set up variables to represent the cost of apples and bananas, and use the given information to create equations.

• After attempting to solve the equations using elimination, they realize that the system is inconsistent and there is no solution.