Answers:
a = -2
b = -1
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Step-by-step explanation:
The first piece 5 must match up with the ax+b when x = -2, or else the function wouldn't be continuous at this junction.
Plug in x = -2 and set the result equal to 5
We end up with -2a+b = 5
Solving for b gets us b = 5+2a
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The middle piece ax+b must also equal the third piece -5 when x = 3 to ensure the second junction is continuous.
This leads us to the equation 3a+b = -5
Apply substitution and solve for 'a'
3a+b = -5
3a+5+2a = -5
5a+5 = -5
5a = -5-5
5a = -10
a = -10/5
a = -2 is one of the answers
Then use this to find b
b = 5+2a
b = 5+2(-2)
b = 5-4
b = -1 is the other answer