Question

Which ordered pairs in the form (x, y) are solutions to the equation

7x−5y=28?

Select each correct answer.

Responses

(7, 9)
Begin ordered pair 7 comma 9 end ordered pair

(−1, −7)
Begin ordered pair negative 1 comma negative 7 end ordered pair

(−6, −14)
Begin ordered pair negative 6 comma negative 14 end ordered pair

(4, 10)

Answer 1

Which statement about the ordered pairs (3, −8) and (4, 4) is true for the equation 3x−y/4=11?

Responses

(4,  4) is a solution to the equation but not (3, −8).
Begin ordered pair 4 comma 4 end orderd pair, is a solution to the equation but not , Begin ordered pair 3 comma negative 8 end ordered pair, .

Both ordered pairs are solutions.
Both ordered pairs are solutions.

Neither ordered pair is a solution.
Neither ordered pair is a solution.

(3, −8) is a solution to the equation but not (4, 4).

Answer 2

To check if an ordered pair (x, y) is a solution to the equation 7x - 5y = 28, substitute the values of x and y into the equation and see if it results in a true statement.

Let's check each ordered pair:

1. (7, 9)
Substituting x = 7 and y = 9:
7(7) - 5(9) = 49 - 45 = 4
4 does not equal 28.

2. (-1, -7)
Substituting x = -1 and y = -7:
7(-1) - 5(-7) = -7 + 35 = 28
28 equals 28.

3. (-6, -14)
Substituting x = -6 and y = -14:
7(-6) - 5(-14) = -42 + 70 = 28
28 equals 28.

4. (4, 10)
Substituting x = 4 and y = 10:
7(4) - 5(10) = 28 - 50 = -22
-22 does not equal 28.

Therefore, the correct ordered pairs that are solutions to the equation are:

(−1, −7)
(−6, −14)

Answer 3

To determine which ordered pairs are solutions to the equation 3x - y/4 = 11, we need to substitute the x and y values of each ordered pair into the equation and check if the equation holds true.

Let's go through each of the given ordered pairs:

1. (3, -8)
Substituting x = 3 and y = -8 into the equation:
3(3) - (-8)/4 = 9 + 2 = 11
So, (3, -8) is a solution to the equation.

2. (4, 4)
Substituting x = 4 and y = 4 into the equation:
3(4) - (4)/4 = 12 - 1 = 11
So, (4, 4) is a solution to the equation.

Therefore, both ordered pairs (3, -8) and (4, 4) are solutions to the equation.