# Thread: Does this have one solution or inifinte

1. ## Does this have one solution or inifinte

x − 3y + z = 1
x + y + 2z = 14

1 -3 1 | 1
1 1 2 | 14

1 -3 1 | 1
0 4 1 | 13

1 -3 1 | 1
0 1 1/4 | 13/4

1 0 7/4 | 43/4
0 1 1/4 | 13/4

So x = 43/4 y = 13/4 and z = 0. Which is one solution.

But because there is 1 variable in my last reuction does this mean there are infinite solutions?

2. it has infinite numbers of solutions, for any value of z u have different values of x,y
it is clear from the beginning since u have three variables and two equations

3. you can do it so that for "z" there is different type of solutions

$x-3y= 1-z$

$x+y = 14-2z$

than depending on your determinants $D, D_x, D_y$ you discuss what can be and how many solutions