Need help with Alg 2 problem

x=7y

x+y+z=80

2x-y+z=105

Isolate and substitute

(7y)+y+z=80

8y+z=80

z=80-8y

2(7y)+y+(80-8y)=105

14y+y-8y=25

15y-8y=25

7y=25

y=25/7

x = 7y

x + y + z = 80

2x - y + z = 105  →  z  = 105 - 2x + y     (3)

Subbing the first equation into the second, we have

7y + y + z  = 80   →  8y + z = 80      (4)

And subbing the first into (3) we have

z = 105 - 2(7y) + y

z = 105 - 13y      (5)

Put (5)  into (4)

8y + 105 - 13y  = 80

-5y  = -25    →  y =  5

And  z = 105 - 13(5)  = 105 - 65  = 40

And x = 7y = 7(5)  = 35

So (x, y, z)  = (35, 5, 40)

Thanks both of you!