Matrix question (WHY ?)

Question

anonymous · Answer

Question :
3x + 7y =2 
6x+14y = 4

*Question has coincident lines, infinitely many solutions*

Answer:
$$(k,\frac{ 2-3k }{ 7 }) ; k \in R$$

Explain the answer briefly

anonymous · Answer

@hba

aravindg · Answer

do u see any similarity between first two equations?

anonymous · Answer

yea, 1/2 = 1/2 = 1/2 and I don't understand the answer given

anonymous · Answer

So what are we solving for here?

callisto · Answer

*Question has coincident lines, infinitely many solutions*
^ You understand this, right?

anonymous · Answer

(k,2−3k7);k∈R what does this means ?

anonymous · Answer

k = any real numbers.
Since it has infinitely many solutions, any number lying on the line 3x + 7y =2 is the solution.
Suppose x=k, sub x=k into 3x + 7y =2 
y = (2-3k)/7

So, the corresponding solution pair is (k,  (2-3k)/7)  for all real k.