Write as a Vector Equality x+y=3 , y=x^2-9

Problem

{[x+y=3],[y=x2−9])

Solution

1. Rearrange the first equation to isolate the variables on one side and the constant on the other.

x+y=3

2. Rearrange the second equation by moving the variable term x2 to the left side to match the structure of the first equation.

−x2+y=−9

3. Define the vector of variables and the vector of constants based on the system of equations.

v=[[x+y],[−x2+y]]

c=[[3],[−9]]

4. Equate the two vectors to form a single vector equality representing the system.

[[x+y],[y−x2]]=[[3],[−9]]

Final Answer

[[x+y],[y−x2]]=[[3],[−9]]

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