Answer:
Step-by-step explanation:If we add the first and second equations, we will eliminate both the x and the y.
(2x + y + z) + (2x - y - z) = (3) + (9)
2x + y + z + 2x - y - z = 3 + 9
4x = 12
x = 3
So, x must equal 3.
Now, if we put 3 into each equation, we have the following equations:
6 + y + z = 3
6 - y - z = 9
3 + y - z = 0
Now, we can move all the numbers to the right side:
y + z = -3
-y - z = 3
y - z = -3
Now, we can try to eliminate another variable. If we add the second two equations, we can eliminate y.
(-y - z) + (y - z) = (3) + (-3)
-y -z + y - z = 0
-2z = 0
z = 0 (because, if we divide both sides by -2 to isolate z, 0/[-2] = 0)
So, now we have x = 3 & z = 0.
Now, pick any of the original equations and plug these values of x & z in, and you will get y.
2x + y + z = 3
2(3) + y + 0 = 3
6 + y + 0 = 3
6 + y = 3
y = -3
So, now we have x = 3, y = -3, & z = 0.
These are the only x, y, and z values that work for all 3 equations
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