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
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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)
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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.