Problem in linear algebra

Question

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

X+5y = -1

x-y = 2

x+3y = 3

A. infinitely many

B. two distinct solutions

C. unique

D. no solution

Answer 1

You don't need always matrix help to know about the solution of linear equations...when equation are complex like with 3 or more unknown variables , go to matrix help center.

Here as number og unknown variables are only 2 , solve it directly like , solve two equations and get value of X and y , now if check if those values satisfy third equation or not...

x-y=2 and x+3y=3 gives y=1/4 x=9/4   

put in x+5y=-1 .....don't satisfy then No solution satisfy then unique solution..

if number of linearly independent equations less than number of unknown variables => infinite solutions...