Consider the following system of linear equations.
$$ x_1+2 x_2=b_1 ; 2 x_1+4 x_2=b_2 ; 3 x_1+7 x_2=b_3 ; 3 x_1+9 x_2=b_4 $$
Which one of the following conditions ensures that a solution exists for the above system?
- A
$b_2=2 b_1$ and $3 b_1-6 b_3+b_4=0$
- B
$b_3=2 b_1$ and $6 b_1-3 b_3+b_4=0$
- C
$b_2=2 b_1$ and $6 b_1-3 b_3+b_4=0$
- D
$b_3=2 b_1$ and $3 b_1-6 b_3+b_4=0$
✓ Correct answer: C
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