y = -4x,        (1)
y =  2x + 3     (2)

Since the left sides of these equations are identical, their right sides are equal.
Therefore, you can write this equation

-4x = 2x + 3,

which says that the right sides are equal.

Now you have a single equation in only one unknown "x", and you can easily solve it by simplifying

-4x - 2x = 3,

-6x = 3,

x = ,

x = .

So, you just found x. It is x = .

Now you can easily find y from (1): y = -4x =  = 2.

Answer.  x = ,  y = 2.