Question 766025
Use the substitution method to solve a
system of equations that has three
variables. 
<pre>
[1]           6x - 4y + 5z = 31
[2]           5x + 2y + 2z = 13
[3]            x +  y +  z =  2

Solve [3] for one of the letters.
I'll pick z

[3]            x +  y +  z =  2
[4]                      z =  2 - x - y

Using [4], Substitute 2 - x - y 
for z in [1]

[1]           6x - 4y + 5z = 31
    6x - 4y + 5(2 - x - y) = 31
    6x - 4y + 10 - 5x - 5y = 31
               x - 9y + 10 = 31
[5]                 x - 9y = 21
 
Using [4], Substitute 2 - x - y 
for z in [2]

[2]           5x + 2y + 2z = 13   
    5x + 2y + 2(2 - x - y) = 13
     5x + 2y + 4 - 2x - 2y = 13
                    3x + 4 = 13
                        3x = 9
[6]                      x = 3
Using [6], Substitute 3 
for x in [5]

[5]                 x - 9y = 21
                    3 - 9y = 21
                       -9y = 18
[7]                      y = -2

Using [6] and [7], Substitute 3 
for x and -2 for y in [5] in [4]

[4]                      z = 2 - x - y
                         z = 2 - 3 - (-2)
                         z = 2 - 3 + 2
[8]                      z = 1

Answer: 

[6]                      x = 3
[7]                      y = -2
[8]                      z = 1

Edwin</pre>