15PTS QUICK Which system of equations has the same solution as the system below? 4x+ 5y = 13 10x – 8y = -32

Question

15PTS QUICK

Which system of equations has the same solution as the system below?
4x+ 5y = 13
10x – 8y = -32

A 4x+ 5y= 13
5x – 4y = -32
B 40x + 50y = 130
5x – 4y = 16
C 20x + 25y = 65
-20x + 16y = 64
D -4x – 5y = 13
10x – 8y = -32

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Aubrey 2 weeks 2021-10-04T09:44:26+00:00 1 Answer 0

Answers ( )

    0
    2021-10-04T09:46:18+00:00

    Answer:

    Option B

    40x + 50y = 130

    5x – 4y = 16

    Option C

    20x + 25y = 65

    -20x + 16y = 64

    Step-by-step explanation:

    we have

    4x+5y=13 —-> equation a

    10x-8y=-32 —-> equation b

    we know that

    If two system of equations are equivalent, then their solution is the same

    Part 1)

    step 1

    Multiply by 10 equation a both sides

    10(4x+5y)=10(13)

    40x+50y=130 —-> equation a’

    step 2

    Divide by 2 equation b both sides

    (1/2)(10x-8y)=(1/2)(-32)

    5x-4y=-16 —-> equation b’

    so

    The system of equations a and b and the system of equations a’ and b’ are equivalent

    therefore

    The system of equations a’ and b’ have the same solution as the given system

    Part 2)

    step 1

    Multiply by 5 equation a both sides

    5(4x+5y)=5(13)

    20x+25y=65 —-> equation a’

    step 2

    Multiply by -2 equation b both sides

    -2(10x-8y)=-2(-32)

    -20x+16y=64 —-> equation b’

    so

    The system of equations a and b and the system of equations a’ and b’ are equivalent

    therefore

    The system of equations a’ and b’ have the same solution as the given system

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