Solving set of linear equations

[slum718]

Homework Statement

x=.5x + .3y +.2z
y= .4x + .4y + .3z
z= .1x + .3y + .5z

x+y+z=1

Homework Equations

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

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

 

[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.