Question 1198522
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The response from tutor @MathLover1 shows that she knows how to find the answer; but it does little to help the student LEARN HOW.<br>
For this particular problem, I would start by factoring out the common factor in each of the first two equations to find that they are equivalent:<br>
x-y-2z=-1 [1]<br>
This means there are only two equations with three unknowns; so we are going to have a solution that is a family of equations instead of a unique solution.<br>
Use equation [1] and the third given equation to eliminate one of the variables.  Arbitrarily I chose to eliminate x:<br><pre>
  -2x+3y+ z= 7
   2x-2y-4z=-2
  -------------
       y-3z= 5 --> y=3z+5</pre>
Substitute y=3z+5 in [1] to find x in terms of z:<br>
x-(3z+5)-2z=-1
x-3z-5-2z=-1
x=5z+4<br>
ANSWER:
x=5z+4
y=3z+5
z=z<br>
Or a better format for the answer would be to use a parameter t:<br>
z=t
x=5t+4
y=3t+5<br>