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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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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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Mathematics
3 years
2021-08-09T14:57:22+00:00
2021-08-09T14:57:22+00:00 1 Answers
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Answers ( )
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