Write as a Vector Equality 3y=9x+6 , 3x-y=-2

Problem

3*y=9*x+6,3*x−y=−2

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting 9*x from both sides.

−9*x+3*y=6

2. Organize the system of linear equations so that the variables x and y are aligned.

−9*x+3*y=6

3*x−y=−2

3. Express the system as a linear combination of constant vectors multiplied by the variables x and y

x*[[−9],[3]]+y*[[3],[−1]]=[[6],[−2]]

4. Identify that the second column is a scalar multiple of the first, and the constant vector is also a multiple, but the task requires the standard vector equation form.

Final Answer

x*[[−9],[3]]+y*[[3],[−1]]=[[6],[−2]]

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