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Find the ordered triplet (x,y,z) for the following system of equations:

x + 3y + 2z = 1

-3x - y + 5z = 10

-2x - 3y + 2z = 7

 May 26, 2021
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(1) - (3) => 3x + 6y = -6

x + 2y = -3

(1) * 5 - (2) * 2 = (5x + 15y + 10z = 5) - (-6x - 2y + 10z = 20) => -x + 13y = -15 => x - 13y = 15

x + 2y = -3

x - 13y = 15

15y = - 18

y = - 6/5

x - 12/5 = -3

x = -15/5 + 12/5 = - 3/5

-3/5 + 3(-6/5) + 2z = 1

-3/5 - 18/5 + 2z = 1

-21/5 + 2z = 1

2z = 24/5

z = 12/5

(-3/5, -6/5, 12/5)

 May 26, 2021

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