if 5b=6a+16 and 9a=7b-20, then what are the values of a and b? show work. can someone help me pls

Question

if 5b=6a+16 and 9a=7b-20, then what are the values of a and b? show work.
can someone help me pls

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Thái Dương 3 years 2021-08-09T14:57:22+00:00 1 Answers 4 views 0

Answers ( )

  1. Adela
    0
    2021-08-09T14:59:21+00:00
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    Answer:

    a = 4, b = 8

    Step-by-step explanation:

    Rewrite 5b=6a+16 and 9a=7b-20 vertically:

    5b=6a+16

    9a=7b-20

    Let’s use substitution.  Solve the first equation for b:

           6a + 16

    b = ————–

                 5

    Substitute this result into the second equation:

    9a = 7(b) + 16, or

                 6a + 16

    9a = 7*————– – 20

                       5

    Eliminate the fraction by multiplying all three terms by 5:

    45a = 7(6a + 16) – 100, or

    3a =        112 – 100, or:

    3a = 12, which leads to a = 4.  

    Find b by subbing 4 for a in either of the given equations:

    5b = 6(4) + 16, or

    5b = 40, leading to b = 8

    The solution is a = 4, b = 8

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