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

Problem

x−3*y=−9,3*y=x+9

Solution

1. Rearrange the equations into standard form a*x+b*y=c so that the variables x and y are on the left side and the constants are on the right side.

x−3*y=−9

−x+3*y=9

2. Identify the coefficients of x and y to form the coefficient matrix A and the constants to form the vector b

A=([1,−3],[−1,3])

b=([−9],[9])

3. Express the system as a linear combination of vectors by separating the terms containing x and the terms containing y

x*([1],[−1])+y*([−3],[3])=([−9],[9])

4. Rewrite the system in the matrix-vector form A*x=b

([1,−3],[−1,3])*([x],[y])=([−9],[9])

Final Answer

([1,−3],[−1,3])*([x],[y])=([−9],[9])

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