Write as a Vector Equality 5b-1b=-8 , -1a+5b=16

Problem

{[5*b−1*b=−8],[−1*a+5*b=16])

Solution

1. Simplify the first equation by combining the like terms for variable b

5*b−1*b=4*b

4*b=−8

2. Identify the coefficients for each variable a and b in both equations to prepare for vector form.

0*a+4*b=−8

−1*a+5*b=16

3. Express the system as a linear combination of vectors by separating the components of a and b

a*([0],[−1])+b*([4],[5])=([−8],[16])

4. Rewrite the system as a single vector equality where the left side is a vector of the expressions and the right side is a vector of the constants.

([4*b],[−a+5*b])=([−8],[16])

Final Answer

([4*b],[−a+5*b])=([−8],[16])

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