SOLUTION: Can you help me solve: 3b-a=-7 5a+6b=14

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Question 134802This question is from textbook Algebra 1 workbook
: Can you help me solve:
3b-a=-7
5a+6b=14This question is from textbook Algebra 1 workbook

Found 2 solutions by josmiceli, algebrapro18:
Answer by josmiceli(6784) About Me  (Show Source):
You can put this solution on YOUR website!
3b+-+a+=+-7
5a+%2B+6b+=+14
First get them both in the order a first, b second
-a+%2B+3b+=+-7
5a+%2B+6b+=+14
Multiply the 1st equation by 5 and add the equations
-5a+%2B+15b+=+-35
5a+%2B+6b+=+14
21b+=+-+21
b+=+-1 answer
3b+-+a+=+-7
3%2A%28-1%29+-+a+=+-7
-a+=+-4
a+=+4 answer
check:
3b+-+a+=+-7
3%2A%28-1%29+-+4+=+-7
-3+-+4+=+-7
-7+=+-7
5a+%2B+6b+=+14
5%2A4+%2B+6%2A%28-1%29+=+14
20+-+6+=+14
14+=+14
OK

Answer by algebrapro18(206) About Me  (Show Source):
You can put this solution on YOUR website!
You would solve this problem using substitution. The steps for substitution are:

1) Solve one of the equation for an isolated variable.
2) Plug in step 1 into the remaining equation and solve for the one variable.
3) Plug in step 2 into step one and find what the isolated variable is.
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3b - a = -7
5a + 6b = 14

Since 3b - a = -7 has a variable alone we will solve this equation for a.

3b - a = -7
-a = -7 - 3b
a = 7 + 3b

now plug that into 5a + 6b = 14 and solve for b.

5a + 6b = 14 --> Plug in a = 7 + 3b into the second equation
5(7 + 3b) + 3b = 14 --> Distribute the 5 though
35 + 15b + 3b = 14 --> Combine like terms
35 + 18b = 14 --> Subtract 35 from both sides
18b = -21 --> Divide both sides by 18
b = -7/6

Now we plug b = -7/6 into a = 7 + 3b and solve for a.

a = 7 + 3b
a = 7 + 3(-7/6)
a = 7 - 7/2
a = 7/2

so your solution is a = 7/2 and b = -7/6.