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Which statements are true about the ordered pair (−1, 5) and the system of equations?

{x+y=4x−y=−6

Select each correct answer.

Responses

The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true.
The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the first equation because it makes the first equation true.

The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true.
The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the second equation because it makes the second equation true.

The ordered pair (−1, 5) is not a solution to the system because it makes at least one of the equations false.
The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false.

The ordered pair (−1, 5) is a solution to the system because it makes both equations true.
The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the system because it makes both equations true.

User Jpsim
by
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1 Answer

4 votes

Answer:

See below. Please review questions for accuracy and accidental double entries.

Explanation:

Lets interpret "{x+y=4x−y=−6" as:

x + y = 4

x − y = −6

===

Let solve the system for the point both lines intersect.

Isolate x:

x + y = 4

x = 4 - y

Then substitute x:

x − y = −6

(4-y) − y = −6 for x = 4 - y

4 - 2y = -6

-2y = -10

y = 5

Use y = 5 in either equation:

x + y = 4

x + 5 = 4 for y = 5

x = -1

The solution is (-1,5)

===

Questions

1. The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true.

Does x + y = 4 when (-1,5)?

-1 + 5 = 4 YES

TRUE

2. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, [(-1,5)] is a solution to the first equation because it makes the first equation true. As above. Same question.

3. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true.

Does x − y = −6 for (-1,5)?

-1 - 5 = -6 ? YES

TRUE

The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair (-1,5), is a solution to the second equation because it makes the second equation true. As above. Same question.

4. The ordered pair (−1, 5) is not a solution to the system because it makes at least one of the equations false. No. FALSE

5. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false. As above. Same question.

The ordered pair (−1, 5) is a solution to the system because it makes both equations true. TRUE

The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the system because it makes both equations true. As above. Same question.

User Boriqua
by
8.3k points
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