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Gekata [30.6K]
2 years ago
15

Directions: State whether or not (3, -2) is a solution to the following systems.

Mathematics
1 answer:
andrew11 [14]2 years ago
8 0

(3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0, (3, -2) is not a solution to the system of equations  -x - y = -5 and 3x - 4y = 17 and (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6

<h3>How to determine the whether or not (3, -2) is a solution to the following systems?</h3>

The systems of equations are given as:

1. x - 2y = 7 and 2x + 3y = 0

2. -x - y = -5 and 3x - 4y = 17

3. x + y = 1 and x - y = 6

Next, we substitute (3, -2) for (x, y) in the system of equations.

So, we have:

<u>1. x - 2y = 7 and 2x + 3y = 0</u>

3 - 2 * -2 = 7 and 2 * 3 + 3 * -2 = 0

Evaluate

7 = 7 and 0 = 0

The above equation is true

Hence, (3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0

<u>2.- x - y = -5 and 3x - 4y = 17</u>

-3 + 2 = -5 and 3 * 3 + 4 * 2 = 17

Evaluate

- 1 = - 5 and 1 7 = 1 7

The above equation is false

Hence, (3, -2) is not a solution to the system of equations  -x - y = -5 and 3x - 4y = 17

<u>3. x + y = 1 and x - y = 6</u>

3 - 2 = 1 and 3 + 2 = 6

Evaluate

1 = 1 and 5 = 6

The above equation is false

Hence, (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6

Read more about system of equations at:

brainly.com/question/13729904

#SPJ1

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Answer:

The relation is not a function

The domain is {1, 2, 3}

The range is {3, 4, 5}

Step-by-step explanation:

A relation of a set of ordered pairs x and y is a function if

  • Every x has only one value of y
  • x appears once in ordered pairs

<u><em>Examples:</em></u>

  • The relation {(1, 2), (-2, 3), (4, 5)} is a function because every x has only one value of y (x = 1 has y = 2, x = -2 has y = 3, x = 4 has y = 5)
  • The relation {(1, 2), (-2, 3), (1, 5)} is not a function because one x has two values of y (x = 1 has values of y = 2 and 5)
  • The domain is the set of values of x
  • The range is the set of values of y

Let us solve the question

∵ The relation = {(1, 3), (2, 3), (3, 4), (2, 5)}

∵ x = 1 has y = 3

∵ x = 2 has y = 3

∵ x = 3 has y = 4

∵ x = 2 has y = 5

→ One x appears twice in the ordered pairs

∵ x = 2 has y = 3 and 5

∴ The relation is not a function because one x has two values of y

∵ The domain is the set of values of x

∴ The domain = {1, 2, 3}

∵ The range is the set of values of y

∴ The range = {3, 4, 5}

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Step-by-step explanation

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