Write as a Vector Equality (4-x)=y^2 , (x-2y)=4

Problem

{[4−x=y2],[x−2*y=4])

Solution

1. Rearrange the equations so that all terms involving variables x and y are on one side and constants are on the other.

4−x=y2⇒−x−y2=−4

x−2*y=4

2. Multiply the first equation by −1 to simplify the signs.

x+y2=4

x−2*y=4

3. Identify the components for the vector representation by grouping the left-hand side expressions into one vector and the right-hand side constants into another.

[[x+y2],[x−2*y]]=[[4],[4]]

4. Decompose the left-hand side into a sum of vectors or a matrix-vector product if possible, though a single vector equality is the standard representation for a system.

[[x],[x]]+[[y2],[−2*y]]=[[4],[4]]

Final Answer

[[4−x],[x−2*y]]=[[y2],[4]]

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