Question

Select the correct responses in the table. The relationship between two numbers is described below, where x represents the first number and y represents the second number. The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to the first number multiplied by 7. Select the equations that form the system that models this situation. Then, select the solution(s) of the system.

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Answer 1

9514 1404 393

Answer:

• x² = y + 16
• 4y - 1 = 7x
• (5, 9)

Explanation:

Writing equations from words is mostly a matter of understanding what the English words mean.

If the first number is x, then the square of the first number is x². That is said to be equal to the sum of the second number (y) and 16:

x² = y + 16 . . . . the first equation

The wording "the difference of A and B" is usually intended to be interpreted to mean A-B. Here, we have the difference of 4 times the second number (4y) and 1, so ...

4y -1

This is equal to the first number (x) multiplied by 7, so ...

4y -1 = 7x . . . . the second equation

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These can be solved a variety of ways. When no method is specified, I like to use a graphing calculator. It shows the only integer solution for this pair of equations is ...

(x, y) = (5, 9)