The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+12 votes
1.2k views

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
asked in Linear Algebra by Veteran (59.7k points) | 1.2k views

4 Answers

+17 votes
Best answer
answer = C

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

rank = total number of variables
Hence, unique solution
answered by Boss (30.9k points)
selected by
+1
Number of free variables=n-r=2-2=0, so no infinite, only unique solutions.
+14 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
answered by Veteran (55.6k points)
+2 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 :)

answered by Junior (911 points)
0 votes

$2X2$  Minor with Determinant non - zero.

answered by Active (3.4k points)
edited by
Answer:

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

44,199 questions
49,669 answers
163,552 comments
65,818 users