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Ammimochi

Solve for x in x+ 3y + 2z = 8

x = 8 - 3y - 2z

Substitute x = 8 - 3y - 2z into 3x + y +3z = -10

24 - 8y - 3z = -10

Substitute x = 8 - 3y - 2z into -2x - 2y - z = 10

-16 + 4y + 3z = 10

Solve for y in 24 - 8y - 3z = -10

y = -3z - 34/8

Substitute y = -3z - 34/8 into x = 8 - 3y - 2z

x = 8 + 3(3z - 34)/8 - 2z

Substitute y = -3z - 34/8 into -16 + 4y + 3z = 10

-16 + -3z + 34/2 + 3z = 10

Solve for z in -16 + -3z + 34/2 = 3z = 10

z = 6

Substitute z = 6 into x = 8 + 3(3z - 34)/8 - 2z

x = -10

Substitute z = 6 into y = -3z - 34/8

y = 2

Therefore,

x = -10

y = 2

z = 6

D. -10, 2, 6

gmany

[tex]\left\{\begin{array}{ccc}x+3y+2z=8&|\text{subtract 3y and 2z from both sides}\\3x+y+3z=-10\\-2x-2y-z=10\end{array}\right\\\\x=8-3y-2z\\\\\text{Substitute it to the second and third equation:}\\\\\left\{\begin{array}{ccc}3(8-3y-2z)+y+3z=-10\\-2(8-3y-2z)-2y-z=10\end{array}\right\\\\\text{use distributive property}[/tex]

[tex]\left\{\begin{array}{ccc}24-9y-6z+y+3z=-10&|\text{subtract 24 from both sides}\\-16+6y+4z-2y-z=10&|\text{add 16 to both sides}\end{array}\right\\\\\text{combine like terms}\\\\\left\{\begin{array}{ccc}-8y-3z=-34\\4y+3z=26&|\text{multiply both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-8y-3z=-34\\8y+6z=52\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad3z=18\qquad\text{divide both sides by 3}\\.\qquad\qquad\boxed{z=6}[/tex]

[tex]\text{Put the value of z to the second equation:}\\\\4y+3(6)=26\\\\4y+18=26\qquad\text{subtract 18 from both sides}\\\\4y=8\qquad\text{divide both sides by 4}\\\\\boxed{y=2}\\\\\text{Put the values of z and y to the equation}\ x=8-3y-2z:\\\\x=8-3(2)-2(6)\\\\x=8-6-12\\\\\boxed{x=-10}\\\\Answer:\ \boxed{x=-10,\ y=2,\ z=6\to(-10,\ 2,\ 6)}[/tex]

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