+1234 Find the ordered quintuplet $(a,b,c,d,e)$ that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 47
2a + 3b + 4c + 5d = 22
3a + 4b + 5c = -17
4a + 5b = 2
5a = 30
+129771 5a = 30 4(6) + 5b =2 3(6) + 4(-22/5) + 5c = -17
a = 6 b = -22/5 -88/5 + 5c = -35
-88 + 25c = -175
25c = -87
c = -87/25
2(6) + 3(-22/5) + 4 (-87/25) + 5d = 22 a + 2b + 3c + 4d + 5e = 47
12 - 66/5 - 348/25 + 5d = 22 6 - 44/5 - 261/25 + 3712/125 + 5e = 47
5d - 378/25 =22 2057 / 125 + 5e = 47
5d = 22 + 378/25 2057 + 625e = 5875
125d = 550 + 378 625e = 3818
125d = 928 e = 3818 / 625
d = 928 / 125
