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Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations

 

a+2b+3c+4d+5e=41

2a+3b+4c+5d = 34

3a+4b+5c =15

4a+5b = 16

5a = 20

 May 1, 2024
 #1
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5a = 20

a = 4

 

4a + 5b = 16

4(4) + 5b = 16

5b = 0

b = 0

 

3a + 4b + 5c = 15

3(4) + 4(0) + 5c = 15

5c = 3

c = 3/5

 

2a + 3b + 4c + 5d = 34

2(4) + 3(0) + 4(3/5) + 5d = 34

5d = 118/5

d = 118/25

 

a + 2b + 3c + 4d + 5e = 41

4 + 2(0) + 3(3/5) + 4(118/25) + 5e = 41

5e = 408/25

e = 408/125

 May 1, 2024

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