Answer:
(x, y, z) = (8, 5, -9)
Step-by-step explanation:
Using the first equation, we can write an expression for z:
z = 12 -2x -y
We can substitute this into the other two equations. (Before we do that, we'll divide the second equation by 5.)
x + y + (12 -2x -y) = 4 ⇒ -x +12 = 4
x -4y +(12 -2x -y) = -21 ⇒ -x -5y +12 = -21
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The first of these gives us a value for x:
8 = x . . . . add x-4 to both sides
Using this in the second equation of these, we have ...
-8 -5y +12 = -21
-5y = -25
y = 5
Then the value of z is ...
z = 12 -2(8) -5
z = -9
The solution to the system is (x, y, z) = (8, 5, -9).
