Write as a Vector Equality 3x^2+y^2=28 , 3x^2-18x+y^2+27=19

Problem

3*x2+y2=28,3*x2−18*x+y2+27=19

Solution

1. Identify the variables and the structure of the equations to represent them in vector form ƒ*(x)=c

2. Define the vector of variables x as a column vector containing the unknowns x and y

x=[[x],[y]]

3. Construct the vector-valued function ƒ*(x) by placing the left-hand side expressions of the equations into a single vector.

ƒ*(x)=[[3*x2+y2],[3*x2−18*x+y2+27]]

4. Construct the constant vector c using the values from the right-hand side of the equations.

c=[[28],[19]]

5. Equate the function vector to the constant vector to form the final vector equality.

[[3*x2+y2],[3*x2−18*x+y2+27]]=[[28],[19]]

Final Answer

[[3*x2+y2],[3*x2−18*x+y2+27]]=[[28],[19]]

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