Question

Brendan and his brother are playing a guessing game. Brendan tells his brother that he is thinking of two negative integers. The first number minus the second number is 3. The square of the first number minus 3 times the second number is equal to 19.

Answer 1

In the guessing game, let x and y represent the two negative integers. The system of equations is x - y = 3 and
`\(x^2 - 3y = 19\)`, defining the difference between the numbers and their quadratic relationship.

Brendan's guessing game involves two negative integers, denoted as x and y. The first equation, x - y = 3, expresses that the first number minus the second is equal to 3. The second equation,
`\(x^2 - 3y = 19\)`, reflects the condition that the square of the first number minus three times the second number equals 19.

This system of equations captures the relationships between the unknown integers, enabling Brendan and his brother to determine the specific values for x and y that satisfy both conditions, ultimately revealing the chosen pair of negative integers in their game.

The complete question is:

Brendan and his brother are playing a guessing game. Brendan tells his brother that he is thinking of two negative integers. The first number minus the second number is 3. The square of the first number minus 3 times the second number is equal to 19. a. Write a system of equations for the situation.