Write as a Vector Equality y=3x-2 , y=2x-3

Problem

y=3*x−2,y=2*x−3

Solution

1. Identify the system of linear equations as a vector equation of the form y=x*a+b or by representing the variables as a vector.

2. Rewrite each equation so that the variables and constants are aligned.

y=3*x−2

y=2*x−3

3. Express the system in vector form by grouping the components of the left side and right side into column vectors.

[[y],[y]]=[[3*x−2],[2*x−3]]

4. Decompose the right-hand side vector into a term containing the variable x and a constant vector.

[[y],[y]]=[[3*x],[2*x]]+[[−2],[−3]]

5. Factor out the scalar x from the first vector on the right side to complete the vector equality.

[[y],[y]]=x*[[3],[2]]+[[−2],[−3]]

Final Answer

[[y],[y]]=x*[[3],[2]]+[[−2],[−3]]

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