Find-the-value-of-a-b-c-d-e-in-the-system-of-equations-13a-2b-c-6d-2e-96-5a-9b-2c-7d-3e-75-7a-8b-17c-11d-7e-99-3a-3b-3c-d-8e-55-a-7b-6c-4d-9e-79-

Question Number 189132 by Shrinava last updated on 12/Mar/23

Find the value of a + b + c + d + e

in the system of equations :

{\begin{cases} 13 a + 2 b + c + 6 d + 2 e = 96 \\ 5 a + 9 b + 2 c + 7 d + 3 e = 75 \\ 7 a + 8 b + 17 c + 11 d + 7 e = 99 \\ 3 a + 3 b + 3 c + d + 8 e = 55 \\ a + 7 b + 6 c + 4 d + 9 e = 79 \end{cases}

Answered by mr W last updated on 12/Mar/23

s a y f = a + b + c + d + e

\Rightarrow a + b + c + d + e - f = 0 \dots (6)

D = | \begin{matrix} 13 & 2 & 1 & 6 & 2 & 0 \\ 5 & 9 & 2 & 7 & 3 & 0 \\ 7 & 8 & 17 & 11 & 7 & 0 \\ 3 & 3 & 3 & 1 & 8 & 0 \\ 1 & 7 & 6 & 4 & 9 & 0 \\ 1 & 1 & 1 & 1 & 1 & - 1 \end{matrix} | = 7047

D_{f} = | \begin{matrix} 13 & 2 & 1 & 6 & 2 & 96 \\ 5 & 9 & 2 & 7 & 3 & 75 \\ 7 & 8 & 17 & 11 & 7 & 99 \\ 3 & 3 & 3 & 1 & 8 & 55 \\ 1 & 7 & 6 & 4 & 9 & 79 \\ 1 & 1 & 1 & 1 & 1 & 0 \end{matrix} | = 98172

\Rightarrow f = a + b + c + d + e = \frac{D_{f}}{D} = \frac{98172}{7047} = \frac{404}{29} ✓

Commented by manxsol last updated on 12/Mar/23

I n e v e r s a w t h a t a r t i f i c e .

t o d a y i s g r e a t!

Commented by mr W last updated on 13/Mar/23

i t h i n k t h i s m e t h o d i s b e t t e r t h a n

s o l v i n g t h e 5 e q u a t i o n s f o r a, b, c, d, e

a n d t h e n c a l c u l a t i n g a + b + c + d + e .

Commented by manxsol last updated on 13/Mar/23

i c a n a n y r e l a t i o n b e t w e e n t h e v a r i a b l e s v e r y, v e r y g o o d S i r W .

Commented by Shrinava last updated on 13/Mar/23

thankyou dearProfessor cool