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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 + e = 15

3a + 4b + 5c + 1d + 2e = 34

4a + 5b + 1c + 2d + 3e = 68

5a + 1b + 2c + 3d + 4e = 57

 May 16, 2023
 #1
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(a,b,c,d,e) = (2,-4,6,1,5)

 May 16, 2023
 #2
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Add equations together to get 15(a+b+c+d+e)=215.

Divide to get a+b+c+d+e=43/3.

Now take equation 1, subtract it from equation 2.

a+b+c+d-4e=-26. Subtract the two equations shown to get 5e=121/3, so e=121/15.

See if you can use this same method to determine a, b, c, and d.

 May 17, 2023

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