Write as a Vector Equality 6xy-4y^2=-4 , 9x^2+4y^2=10

Problem

{[6*x*y−4*y2=−4],[9*x2+4*y2=10])

Solution

1. Identify the components of the vector system by grouping the left-hand side expressions and the right-hand side constants into separate column vectors.

2. Define the vector function F(x,y) using the expressions from the left side of the equations.

F(x,y)=[[6*x*y−4*y2],[9*x2+4*y2]]

3. Define the constant vector b using the values from the right side of the equations.

b=[[−4],[10]]

4. Equate the two vectors to represent the system as a single vector equality.

[[6*x*y−4*y2],[9*x2+4*y2]]=[[−4],[10]]

Final Answer

[[6*x*y−4*y2],[9*x2+4*y2]]=[[−4],[10]]

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