SOLUTION: Solve the system of equations. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.) x + y − 7z = −1 y − z = 0 −

Second equation says  y = z.


Using it, replace z in the first equation by y.  

You will get the first equation in the form


    x + y - 7y = -1,   or

    x - 6y = -1.


It is the same as (or equivalent to) the third equation.


It means that the system has infinitely many solutions.


We can take z as a free variable, to which we can give any value.


Then  y = z  and  x = (from the very first equation)  -1 - y + 7z = -1 - z + 7z = -1 + 6z.


Thus the general formulas for the infinite numbers of solutions is


    (x,y,z) = (-1+6z, z, z).      


ANSWER.  There are infinitely many solutions.


         The general formula for the solutions is  (x,y,z) = (-1+6z,z,z).