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+15 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
in Linear Algebra by Veteran (52.1k points) | 1.6k views

4 Answers

+21 votes
Best answer
answer = C

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

rank = total number of variables
Hence, unique solution
by Boss (30.5k points)
selected by
Number of free variables=n-r=2-2=0, so no infinite, only unique solutions.

I think for any set of linear non homogeneous equations two distinct solutions (option B) can never be possible..


+17 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
by Veteran (60k points)

@ sir, for given this type of equation i.e non-homogeneous eqn, how can I distinguish b/w infinitely many & no solution.

+3 votes


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 :)

by Junior (905 points)
how all equations are linearly independent.

multiplying -2 with eqn no. 2 & then add with eqn. no. 3 we'll get eqn no. 1

-2*(eqn2)+(eqn3) = (eqn1)
0 votes

$2X2$  Minor with Determinant non - zero.

by Active (4.7k points)
edited by

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