math help...?

Question

i am studying for a test, how do you do this problem?

find a general expression for all of its solutions
x-2y+3z=1
x+y-3z=7
3x-4y+5z=7

the answer is (5+z, 2+2z, z) but i need to know how to solve it

Answer 1

x-2y+3z=1....[1]
x+y-3z=7......[2]
3x-4y+5z=7....[3]

[1]-[2]
-3y +6z = -6
so y = 2z+2

Put that in to [2]
x-z=5
so x=5+z

so x, y, z are 5+z, 2+2z, z, respectively.
.

Answer 2

x-2y+3z=1 <-- Eq1
x+y-3z=7 <-- Eq 2
3x-4y+5z=7 <-- Eq 3
3x-3z = 15 <-- Eq 1+2*Eq 2
3x= 3z +15
x = z+5
-7y+14z = -14 <-- Eq 3 -3 Eq 2
-y =-2z-2
y = 2z+2
So (z+5, 2z+2,z)