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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=15

3a+4b+5c=34

4a+5b=63

5a=57

 Jun 12, 2024
 #1
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5a = 57

a = 11.4

 

4(11.4) + 5b = 63

45.6 + 5b = 63

5b = 17.4

b = 3.48

 

3(11.4) + 4(3.48) + 5c = 34

34.2 + 13.92 + 5c = 34

48.12 + 5c = 34

5c = -14.12

c = -2.824

 

2(11.4) + 3(3.48) + 4(-2.824) + 5d = 15

22.8 + 10.44 - 11.296 + 5d = 15

21.944 + 5d = 15

5d = -6.944

d = -1.3888

 

11.4 + 2(3.48) + 3(-2.824) + 4(-1.3888) + 5e = 47

11.4 + 6.96 - 8.472 - 5.5552 + 5e = 47

4.3328 + 5e = 47

5e = 42.6672

e = 8.53344

 

(a, b, c, d, e) = (11.4, 3.48, -2.824, -1.3888, 8.53344)

 Jun 12, 2024

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