Write as a Vector Equality (3y+9)=x , (9-x)=-3y

Problem

{[3*y+9=x],[9−x=−3*y])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting 3*y from both sides.

x−3*y=9

2. Rearrange the second equation into standard form by adding x to both sides.

x−3*y=9

3. Identify the coefficients of x and y to form the coefficient matrix and the constant vector.

([1,−3],[1,−3])*([x],[y])=([9],[9])

4. Express the system as a linear combination of vectors by separating the variables.

x*([1],[1])+y*([−3],[−3])=([9],[9])

Final Answer

x*([1],[1])+y*([−3],[−3])=([9],[9])

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