Answer:
option D
Step-by-step explanation:
3x – 2 = –18 + 5y Equation 1
8y – 6 = 4x + 9y Equation 2
y – 10 = 3x + 2z Equation 3
Using Equation 1 we have:
3X=-18+5Y+2
3X=-16+5Y
[tex]X=\frac{-16+5Y}{3}[/tex] Equation 4
Using Equation 3 we have:
Y-10-3X=2Z
So [tex]Z=\frac{Y-10-3X}{2}[/tex] Equation 5
Using equation 2 and substituting equation 4 we have:
[tex]8Y-6=4(\frac{-16+5Y}{3} )+9Y\\\\8Y-6=\frac{-64}{3}+\frac{20}{3}Y+9Y\\\\8Y-9Y-\frac{20}{3}Y =\frac{-64}{3}+6\\\\-Y-\frac{20}{3}Y =\frac{-46}{3}\\\frac{-23}{3}Y =\frac{-46}{3}\\23Y=46\\Y =\frac{46}{23}=2[/tex]
Using Equation 4 we have:
[tex]X=\frac{-16+5*(2)}{3} =\frac{-16+10}{3}=-2[/tex]
Using Equation 5 we have:
[tex]Z=\frac{2-10-3*(-2)}{2} =-1[/tex]
Finally:
X=-2
Y=2
Z=-1
