Answer:
(x, y, z) = (-3, 2, 5)
Step-by-step explanation:
Using the first equation, we can write an expression for x:
x = 21 +3y -6z
Substituting this into the remaining two equations gives ...
3(21 +3y -6z) +2y -5z = -30
63 +9y -18z +2y -5z = -30
11y -23z = -93
and
2(21 +3y -6z) -5y +2z = -6
42 +6y -12z -5y +2z = -6
y -10z = -48
This second equation makes it easy to write an expression for y:
y = 10z -48
Substituting that into the previous equation, we have ...
11(10z -48) -23z = -93
110z -528 -23z = -93
87z = 435
z = 5
y = 10(5) -48 = 2
x = 21 +3(2) -6(5) = -3
The solution is (x, y, z) = (-3, 2, 5).
