Answer: b = 10 is correct
I don't know how your teacher got 12.
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Step-by-step explanation:
The point (-1,2) means x = -1 and y = 2 pair up together.
Plug those points into the template ax+by = 16 to get -a+2b = 16
We'll come back to this later.
Do the same for the point (4,0) to get 4a+0b = 16 which solves to a = 4
Then plug this value into the other equation and solve for b.
-a+2b = 16
-4+2b = 16
2b = 16+4
2b = 20
b = 20/2
b = 10