Question

Resolva:

$a + 2c = 1 \\ b + 2d = 0 \\ 3a + 4c = 0 \\ 3b + 4d = 1$

Answer 1

$a \ = \ 1 \ - \ 2c \\ \\ Substituindo \ fica: \\ \\ 3\ (1 \ - \ 2c) \ + \ 4c \ = \ 0 \\ \\ 3 \ - \ 6c \ + \ 4c \ = \ 0$

$- \ 6c \ + \ 4c \ = \ - \ 3 \\ \\ - \ 2c \ = \ - \ 3 \\ \\ c \ = \ - \ 3 \ \div \ (- \ 2) \\ \\ c \ = \ 1,5$

$a \ + \ 2 \ * \ (1,5) \ = \ 1 \\ \\ a \ + \ 3 \ = 1 \\ \\ a \ = \ 1 \ - \ 3 \\ \\ a \ = \ - \ 2$

$b \ = \ - \ 2d \\ \\ Substituindo \ fica: \\ \\ 3 \ (- \ 2d)\ + \4d \ = \ 1 \\ \\ - \ 6d \ + \ 4d \ = \ 1 \\ \\ - \ 2d \ = \ 1$

$d \ = \ 1 \ \div \ (- \ 2) \\ \\ d \ = \ - \ 0,5$

$Resposta: \\ \\ a \ = \ - \ 2 \\ \\ b \ = \ 1 \\ \\ c \ = \ 1,5 \\ \\ d \ = \ - \ 0,5$

Answer 2

multiplique a+2c=1 por -3 --------- -3a-6c=-3
subtraia agora de 3a+4c=0
                         -3a-6c=-3
                           0 -2c=-3    ------    c=3/2
se c=3/2 a=-2 ( a+2*3/2=1  ---- a=1-3 ---- a=-2
agora multiplique b+2d=0 por -3 -------  -3b-6d=0 subtraia de 3b+4d=1
3b+4d=1
-3b-6d=0
  0 -2d=1  ------ d=-1/2
se d=-1/2 b=-1 ( b+2d=0 ----- b+2*-1/2=0 ----- b=-1