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Y is equal to positive negative one, and x is equal to negative 1

 y^{2} + 5x = 4 and  y^{2} -3x -4  
multiply negative to the second equation, so as to cancel the y squared, then you will have : 
 y^{2} + 5x = 4 and - y^{2} +3x +4  
simply add them, giving you: 
8x+8=0, solve for x, giving you -1  

substitute -1 to the x of any equation, solve for it, then y= positive negative 1