Write as a Vector Equality x+y=6 , 2x-9y=1

Problem

{[x+y=6],[2*x−9*y=1])

Solution

1. Identify the coefficients of the variables x and y in each equation of the system.

2. Separate the system into a linear combination of two constant vectors, each scaled by one of the variables.

3. Express the first terms as x multiplied by the vector of its coefficients ([1],[2])

4. Express the second terms as y multiplied by the vector of its coefficients ([1],[−9])

5. Equate the sum of these scaled vectors to the vector of constants from the right-hand side of the equations.

Final Answer

x*([1],[2])+y*([1],[−9])=([6],[1])

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