# Solving set of linear equations

1. Sep 20, 2011

### slum718

1. The problem statement, all variables and given/known data
x=.5x + .3y +.2z
y= .4x + .4y + .3z
z= .1x + .3y + .5z

x+y+z=1

2. Relevant equations

when solved, x= 21/62, y=23/62, z= 18/62

3. The attempt at a solution
I've tried doing row reduction but I keep failing ex:
.5 .3 .2
.4 .4 .3
.1 .3 .5
=
0 -1.2 -2.3
.4 .4 .3
.1 .3 .5 I tried many combos of this and I get lost and have no idea how to really go about it

2. Sep 21, 2011

### MisterX

One may represent a system of linear equations as an http://en.wikipedia.org/wiki/Augmented_matrix#Solution_of_a_linear_system".

You failed to correctly represent the system of equations as a matrix. Notice how for the first equation has x on both sides. In the matrix representing the system, there should be one column for coefficient of x. The x on the left side of the first equation should not be ignored. So, first get the equations in the correct form.

Last edited by a moderator: Apr 26, 2017