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kotykmax [81]
3 years ago
7

Suppose that y varies inversely with x. Write a function that models the inverse function x=7 when y=3

Mathematics
1 answer:
anygoal [31]3 years ago
7 0

9514 1404 393

Answer:

  y = 21/x

Step-by-step explanation:

The inverse variation relation means ...

  y = k/x

For the given values, we can determine the constant k:

  3 = k/7

  3×7 = k = 21

Then the function is ...

  y = 21/x

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The solution to the system of equations are (2, 5).

Solution:

The system of equations are

x + y = 7 – – – – (1)

2x – y = –1 – – – – (2)

To find x from equation (1):

x + y = 7

Subtract y from both sides of the equation, we get

⇒ x + y – y = 7 – y

⇒ x = 7 – y – – – (3)

Substitute (3) in (2) we get,

2(7 – y) – y = –1

14 – 2y – y = –1

14 – 3y = –1

Subtract 14 from both sides,

–3y = –15

Divide by –5 on both sides,

y = 5

Substitute y = 5 in equation (3)

x = 7 – 5

x = 2

The solution to the system of equations are (2, 5).

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