Write as a Vector Equality y=x-4 , x+3y=12

Problem

y=x−4,x+3*y=12

Solution

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

−x+y=−4

2. Identify the coefficients of x and y from both equations to form the coefficient matrix.

([−1,1],[1,3])

3. Define the vector of variables and the vector of constants.

x=([x],[y])

b=([−4],[12])

4. Combine the components into a single vector equality of the form A*x=b

([−1,1],[1,3])*([x],[y])=([−4],[12])

Final Answer

([−1,1],[1,3])*([x],[y])=([−4],[12])

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