Write as a Vector Equality x=y+1 , y=3x-1

Problem

{[x=y+1],[y=3*x−1])

Solution

1. Rearrange the equations into standard form so that all variables are on the left side and constants are on the right side.

x−y=1

−3*x+y=−1

2. Identify the coefficients of the variables x and y to form the column vectors for the left side of the equality.

([1],[−3])*x+([−1],[1])*y=([1],[−1])

3. Express the system as a single vector equation by grouping the variables into a vector v=([x],[y]) and the coefficients into a matrix.

([1,−1],[−3,1])*([x],[y])=([1],[−1])

Final Answer

([1,−1],[−3,1])*([x],[y])=([1],[−1])

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