Given a+b=7 and a-b=3, find:

3^a:3^b

a = - 2 and b=3

Step-by-step explanation:

Step 1) Solve the first equation for a:

a + 3b = 7

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

a + 0 = 7 - 3b

a = 7 - 3b

Step 2) Substitute (7 - 3b) for a in a second equation and solve for b:

2a = b - 7 becomes:

2 (7 - 3b) = b-7

(2 multi. 7) - (2 multi. 3b) = b-7

14 - 6b = b - 7

14 + 7 - 6b + 6b = b + 6b = b + 6b - 7 + 7

21 - 0 = 1b + 6b - 0

21 = (1 + 6) b

21 = 7b

21 / 7 = 7b/7

3 = 7b/7

3 = b

b = 3

Step 3) Substitute 3 for b in the solution to the first equation at the end of Step 1 and calculate a:

a = 7 - 3b becomes:

a = 7 - (3 ⋅ 3)

a = 7 - 9

a = - 2

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