If a , b , c and d satisfy the equations: a + 7 b + 3 c

Kenley Wagner

Kenley Wagner

Answered question

2022-05-28

If a, b, c and d satisfy the equations:
a + 7 b + 3 c + 5 d = 0
8 a + 4 b + 6 c + 2 d = 16
2 a + 6 b + 4 c + 8 d = 16
5 a + 3 b + 7 c + d = 16
then ( a + d ) ( b + c ) equals 16.
why ( a + d ) ( b + c ) equals 16?

Answer & Explanation

pralkammj

pralkammj

Beginner2022-05-29Added 7 answers

Summing the second and third equations we get a + b + c + d = 0. Summing the first and fourth, 6 ( a + d ) + 10 ( b + c ) = 16. This is a system in two variables.
Avah Knapp

Avah Knapp

Beginner2022-05-30Added 6 answers

Add equations (2) and (3) to get: 10 a + 10 b + 10 c + 10 d = 0.
Add equations (1) and (4) to get: 6 a + 10 b + 10 c + 6 d = 16.
The first equation tells you a + d = ( b + c ), so that ( a + d ) ( b + c ) = ( a + d ) 2 .
To find ( a + d ), observe that the coefficients of b and c in the above two equations are the same, so you may subtract them to obtain 4 a + 4 d = 16.

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