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

Problem

x+y=−4,y=−3−x−3

Solution

1. Simplify the second equation by combining the constant terms.

y=−x−6

2. Rearrange both equations into standard form a*x+b*y=c to align the variables.

x+y=−4

x+y=−6

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

A=[[1,1],[1,1]]

4. Define the vector of variables x and the vector of constants b

x=[[x],[y]]

b=[[−4],[−6]]

5. Construct the vector equality by multiplying the coefficient matrix by the variable vector and setting it equal to the constant vector.

[[1,1],[1,1]]*[[x],[y]]=[[−4],[−6]]

Final Answer

[[1,1],[1,1]]*[[x],[y]]=[[−4],[−6]]

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