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

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02-07-2018
Mathematics

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

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carlosego carlosego · Answer 1 · 2018-07-11T23:22:14+02:00

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