How do I solve 2x+3y=7, x-y=1

2x+3y=7
x-y=1

2x+3y=7
x=1+y

2*(1+y)+3y=7
x=1+y

2+2y+3y=7
x=1+y

5y=5       |(:5)
x=1+y

y=1
x=2

CHECK:
2x+3y=7
x-y=1

2*2 + 3*1 = 7     

x-y = 1
2-1 = 1

2x+3y=7                                               
2(2)+3y=7                                                                                              
4+3y=7
subtract 4 from both sides                  
3y=3                                             
divide both side by 3                          
y=1
 
2x+3y=7
2x+3=7
2x+3y=7
subtract 3y from both sides
2x=7-3y
divide both side by 2
x=3.5-1.5
x=2                                     

then you do the x-y=1

x-y=1
2-1=1
1=1

in the end both answers are 1 so that means that i did it right. that means that x=2 and y=1