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Question 1014889: Solve the variables and check. Use elimination method.
"3x+y=14+z
3y-16=z-y
x+10=3z-y"
Answer by skippo(9)   (Show Source):
You can put this solution on YOUR website! Solve the variables and check. Use elimination method.
"3x+y=14+z...........I
3y-16=z-y............II
x+10=3z-y"...........III
SOLUTION:
from equation II
3y-16 = z-y
3y+y = z+16
4y = z+16
Z = 4y-16...........IV
substitute 4y-16 for z in equation I
3x+y = 14+4y-16
3x+y-4y = 14-16
3x-3y = -2........V
substitute 4y-16 for z in equation III
x+10 = 3(4y-16)-y
x+10 = 12y-48-y
x+10 = 11y-48
x-11y = -48-10
x-11y = -58..........VI
solve equation V and VI simultaneously
3x-3y =-2
x-11y =-58
multiply equation V by 1 and equation VI by 3
3x-3y = -2...........VII
3x-33y = -174........VIII
subract equation VIII from equation VII to eliminate x
3x-3y-(3x-33y) = -2-(-174)
3x-3y-3x+33y = -2+174
30y = 172
y = 172/30 = 5.73
substitute 5.73 for y in equation IV
z = 4(5.73)-16
z = 22.92-16
z = 6.92
substitute 5.73 for y, 6.92 for z in equation I
3x+5.73 = 14+6.92
3x = 20.92-5.73
3x = 15.19
x = 15.19/3
x = 5.063.
therefore, x = 5.063, y = 5.73, z = 6.92
checking:
3(5.063)+5.73 = 14+6.92
15.19+5.73 = 20.92
20.92 = 20.92
3(5.73)-16 = 6.92-5.73
17.19-16 = 1.19
1.19 = 1.19
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