Understanding Systems of Equations

Arbegla realizes a mistake in the cost of apples and bananas, leading to a reevaluation of the problem. Equations are set up to determine the cost per pound of each fruit. Attempts to solve the equations through elimination result in an identity, indicating infinite solutions. Graphing the constraints reveals the same line, confirming the system's dependency. The bird explains that the same ratio of fruits was bought, leading to consistent but insufficient information.

What was the initial mistake Arbegla realized in the cost calculation?

• The cost of apples was too high.

• The cost of bananas was too low.

• The total cost was incorrectly stated as $3 instead of $5.

• The weight of the apples was incorrect.

What does the variable 'a' represent in the equations?

• The cost of apples per pound.

• The cost of bananas per pound.

• The total weight of apples.

• The total cost of apples and bananas.

What method is used to try to solve the equations?

• Substitution

• Graphing

• Trial and error

• Elimination

What does the result 0 = 0 indicate about the system of equations?

• There is a unique solution.

• The equations are inconsistent.

• There is no solution.

• There are infinite solutions.

What does the bird suggest to better understand the problem?

• Use a different method.

• Recalculate the costs.

• Ask the King for help.

• Graph the equations.

What is revealed when the equations are graphed?

• They are parallel lines.

• They form a triangle.

• They are the same line.

• They intersect at one point.

Why is the system of equations considered dependent?

• Because it has a unique solution.

• Because it is inconsistent.

• Because it has no solutions.

• Because it has infinite solutions.

What additional information is needed to find a unique solution?

• The exact weight of the bananas.

• A different ratio of apples to bananas.

• The total cost of the second trip.

• The price of apples in the second week.

What does a consistent system of equations mean?

• The equations are unrelated.

• The equations are incorrect.

• The equations have at least one solution.

• The equations have no solutions.

What is the significance of the same ratio of apples and bananas being bought in both trips?

• It results in infinite solutions.

• It causes the system to be inconsistent.

• It makes the equations incorrect.

• It leads to a unique solution.