Which ordered triple is a solution of the following linear system? : 2x+3y+2z=26 −x+7y−z=21 3x+2y−5z=13

For this case we have the following system of equations:
 
 From equation 2 we can clear z:
 
 We substitute the values of z in equations 1 and 3:
 
 From here, we obtain a system of two equations with two unknowns, whose graphical solution is given by the intersection of both lines:
 
 Note: See attached image for the graphic solution
 We now look for the value of z replacing the found values of the graphic solution:
 
 Therefore, the triple ordered solution is:
 
 
 
 See attached image