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In such questions, we should be trying to complete the squares.
We see a xy term; we need to accommodate that in a square that has both x and y terms.
Since there is only one other term with x, we also need to have it entirely in the square.
(2x – y)² = 4x² + y² – 4xy
Using this in the given equation, we are left with
(2x – y)² + 3y² + 3 – 6y
This can be written as (2x – y)² + 3(y² + 1 – 2y)
(2x – y)² + 3(y – 1)² = 0
Since both the squares add up to 0, this is only possible when the squares themselves are 0
This would give us y = 1 from the second term, and using that, we get x = 1/2 from the first term.
Therefore the value of 4x + 5y will be 2 + 5 = 7