Write as a Vector Equality -x+3y+6=0 , x-3y=6

Problem

−x+3*y+6=0,x−3*y=6

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by moving the constant term to the right side.

−x+3*y=−6

2. Identify the coefficients of x and y and the constants on the right side for both equations.

Equation 1: −1*x+3*y=−6

Equation 2: *1*x−3*y=6

3. Express the system as a linear combination of vectors by grouping the coefficients of x into one vector and the coefficients of y into another.

x*[[−1],[1]]+y*[[3],[−3]]=[[−6],[6]]

4. Rewrite the system in the matrix-vector form A*x=b by placing the coefficients into a matrix.

[[−1,3],[1,−3]]*[[x],[y]]=[[−6],[6]]

Final Answer

[[−1,3],[1,−3]]*[[x],[y]]=[[−6],[6]]

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