6r-s+ 3t = -9
5r + 5s - 5t= 20
3r-s+ 4t= -5

Explanation:

6r - s + 3t = -9 (1)
5r + 5s - 5t = 20 (2)
3r - s + 4t = -5 (3)

Add (1) and (3)

-1(6r - s + 3t = -9)
3r - s + 4t = -5
—————————
-6r + s - 3t = 9
3r - s + 4t = -5
————————
-3r + t = 4 (4)

Add (2) and (3):

5r + 5s - 5t = 20
5(3r - s + 4t = -5)
—————————
5r + 5s - 5t = 20
15r - 5s + 20t = -25
——————————
20r + 15t = -5 (5)

Add (4) and (5):

-15(-3r + t = 4)
20r + 15t = -5
———————
45r - 15t = -60
20r + 15t = -5
———————
65r = -65
r = -65/65
r = -1

Plug r value in (4):
-3(-1) + t = 4
3 + t = 4
t = 4 - 3
t = 1

Plug r and t value in (3):

3(-1) - s + 4(1) = -5
-3 - s + 4 = -5
1 - s = -5
-s = -6
s = 6

Therefore, r = -1, s = 6 and t = 1