Question 862145
Same system, x must be equal in both equations at the same time; y must be equal in both equations at the same time.  

One equation says 3x+y=7 and the other equation says 3x+y=10.  There is a transitive property of equality which says that  a=b and b=c means that a=c.  This property must seem intuitively correct and therefore perfectly understood.  

Using this transitive property for your given system, 7 is equal to the binomial expression 3x+y; and 10 is equal to the binomial expression 3x+y.  If 7=3x+y and if 3x+y=10, then according to transitive property, 7=10.  You see something wrong now?  At least you should understand that these two equations cannot be in the same system of equations.