using determinant method, what is the value of x in the equations 3x + 2y = "-10" and 5x + 3y = "-16?"

Answer 1

why the quotation marks? They don;t clarify or change anything.
Anyway, you have
D =
|3 2|
|5 3| = -1

Dx =
|-10 2|
|-16 3| = 2

Dy =
|3 -10|
|5 -16| = 2

x = Dx/D = -2
y = Dy/D = -2

as always, check to make sure these values work in the original equations.
They do.