Write as a Vector Equality y-x=1 , y=1/2x+4

Problem

{[y−x=1],[y=1/2*x+4])

Solution

1. Rearrange the equations into standard form a*x+b*y=c so that the variables align.

−x+y=1

−1/2*x+y=4

2. Identify the coefficients of x and y to form the column vectors.
   The coefficients for x are −1 and −1/2
   The coefficients for y are 1 and 1

3. Express the system as a linear combination of these column vectors.

x*[[−1],[−1/2]]+y*[[1],[1]]=[[1],[4]]

4. Rewrite the linear combination as a single vector equality by performing scalar multiplication and vector addition.

[[−x],[−1/2*x]]+[[y],[y]]=[[1],[4]]

[[−x+y],[−1/2*x+y]]=[[1],[4]]

Final Answer

[[−x+y],[−1/2*x+y]]=[[1],[4]]

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