Classify the system of equations. – X=3- y -7+ y = -x-2 NH

Question

Classify the system of equations.

X=3- y
-7+ y = -x-2
NH

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Ayla 3 weeks 2021-09-27T13:28:14+00:00 1 Answer 0

Answers ( )

    0
    2021-09-27T13:29:41+00:00

    Answer:

    Part 1) Is a consistent independent system, because has exactly one solution.

    Part 2) Is a inconsistent system, because has no solution.

    Step-by-step explanation:

    Part 1) we have

    we have

    -x=3-y

    isolate the variable y

    y=x+3 —–> equation A

    -7+y=-x-2

    isolate the variable y

    y=-x-2+7

    y=-x+5 —-> equation B

    Solve the system by elimination

    Adds equation A and equation B

    y=x+3\\y=-x+5\\---------\\y+y=3+5\\2y=8\\y=4

    Find the value of x

    substitute the value of y in equation A or equation B

    4=x+3\\x=1

    The solution is the point (1,4)

    therefore

    Is a consistent independent system, because has exactly one solution.

    Part 2) we have

    we have

    x=3-y

    isolate the variable y

    y=-x+3 —–> equation A

    -7+y=-x-2

    isolate the variable y

    y=-x-2+7

    y=-x+5 —-> equation B

    Compare equation A and equation B

    Line A and Line B have the same slope (m=-1) and different y-intercept

    so

    Line A and Line B are different parallel lines

    The system has no solution

    therefore

    Is a inconsistent system, because has no solution.

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