x - 8y + z = 2 .....multiply by -1
x - 4y + 7z = 7
------------------
-x + 8y - z = -2 (result of multiplying by -1)
x - 4y + 7z = 7
------------------add
4y + 6z = 5
x - 4y + 7z = 7
x + 2y - z = 2.....multiply by -1
------------------
x - 4y + 7z = 7
-x - 2y + z = -2 (result of multiplying by -1)
-----------------add
-6y + 8z = 5
4y + 6z = 5....multiply by 3
-6y + 8z = 5...multiply by 2
-----------------
12y + 18z = 15 (result of multiplying by 3)
-12y + 16z = 10 (result of multiplying by 2)
-----------------add
34z = 25
z = 25/34
4y + 6z = 5
4y + 6(25/34) = 5
4y + 150/34 = 5
4y = -150/34 + 5
4y = -150/34 + 170/34
4y = 20/34
y = 20/136 reduces to 5/34
x - 8y + z = 2
x - 8(5/34) + 25/34 = 2
x - 40/34 + 25/34 = 2
x - 15/34 = 2
x = 2 + 15/34
x = 68/34 + 15/34
x = 83/34
so x = 83/34, y = 5/34, and z = 25/34 <====
