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 adding 6 to both sides.

x+3*y=6

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

1*x+3*y=6

−1*x−3*y=−6

3. Express the system as a linear combination of vectors by grouping the x terms, the y terms, and the constant terms.

x*([1],[−1])+y*([3],[−3])=([6],[−6])

4. Rewrite the system in matrix-vector form A*x=b by placing the coefficients into a 2×2 matrix.

([1,3],[−1,−3])*([x],[y])=([6],[−6])

Final Answer

([1,3],[−1,−3])*([x],[y])=([6],[−6])

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