Im not sure how this works and what gets eliminated

Question

 Solve the system using the Gauss-Jordan method.

–5x + 4y = –14

x – 3y = 16 

Answer 1

-5 4 | -14

1 -3 | 16

step #1: 5 * eq2 + e1 --> eq1

0 -11 | 66

1 -3 | 16

step #2: swap rows; eq #2/-11

1 -3 | 16

0 1 | -6

y = -6

x - 3y = 16

x - 3(-6) = 16

x + 18 = 16

x = -2

{x=-2, y=-6}

check: (-5)(-2) + 4(-6) = 10 + -24 = -14

(-2)-3(-6) = -2 - (-18) = -2 + 18 = 16