8,279 views
28 votes
28 votes

How many solutions does the following system of linear equations have?

  • $-x + 5y = -1$
  • $x - y = 2$
  • $x + 3y = 3$
  1. infinitely many
  2. two distinct solutions
  3. unique
  4. none

4 Answers

Best answer
31 votes
31 votes
answer = C

rank = r(A) = r(A|B) = 2

rank = total number of variables
Hence, unique solution
selected by
23 votes
23 votes
C unique solution..
3 equation , 2 variable.
solve any two equation and check 3rd equation by putting values in 3rd equation.
x = 9/4 , y = 1/4
3 votes
3 votes

DIFFERENT APPROACH

all the equations are linearly independent. i.e non of the equations can be obtained by multiplying one of equation with a number (this means that no two vectors overlap each other leading to a rank of 3). therefore there will be a unique solution. 

Correct me if wrong :)

0 votes
0 votes

rank[A] = 2 and rank[A|B] = 2

it is unique solution .

Answer:

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