Question

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

Answer 1

For this case we have the following system of equations:
 $2x + 3y + 2z = 26 -x + 7y-z = 21 3x + 2y-5z = 13$
 From equation 2 we can clear z:
 $z = -x + 7y-21$
 We substitute the values of z in equations 1 and 3:
 $2x + 3y + 2 (-x + 7y-21) = 26 3x + 2y-5 (-x + 7y-21) = 13$
 From here, we obtain a system of two equations with two unknowns, whose graphical solution is given by the intersection of both lines:
 $x = 5 y = 4$
 Note: See attached image for the graphic solution
 We now look for the value of z replacing the found values of the graphic solution:
 $z = -x + 7y-21 z = -5 + 7 * (4) -21 z = 2$
 Therefore, the triple ordered solution is:
 $(x, y, z) = (5,4,2)$
 Answer:
 $(x, y, z) = (5,4,2)$
 See attached image