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Korvikt [17]
3 years ago
14

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

Mathematics
1 answer:
sergiy2304 [10]3 years ago
5 0
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

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