Write as a Vector Equality 1/3x-y=9 , x-9y=51

Problem

{[1/3*x−y=9],[x−9*y=51])

Solution

1. Identify the coefficients of the variables x and y in each equation to form the column vectors.

2. Extract the coefficients of x from both equations to create the first vector: ([1/3],[1])

3. Extract the coefficients of y from both equations to create the second vector: ([−1],[−9])

4. Identify the constants on the right side of the equations to create the resultant vector: ([9],[51])

5. Combine these components into a single vector equation where the variables x and y scale their respective coefficient vectors.

Final Answer

x*([1/3],[1])+y*([−1],[−9])=([9],[51])

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