The answer to #1 is x = 2, y = 1 and z = -5.
In order to solve this, we need to get variables to eliminate. Sometimes, in order to get things to cancel, we have to multiply equations by factors. For instance, we'll start by cancelling things using the first and second equation. Multiply the first equation by -1 and then add through.
5x + y - z = 16
-5x - y - 4z = 9
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-5z = 25 ----> Divide by -5
z = -5
Now, to get another answer, use the first and third equation. Multiply the first equation by 3 to get them to cancel.
-15x - 3y - 12z = 27
-6x + 3y + 3z = -24
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-21x - 9z = 3
Now we can plug in our value for z to solve for x.
-21x - 9(-5) = 3
-21x + 45 = 3
-21x = -42
x = 2
Now that we have x and z, we can plug into any equation to find y.
-5x - y + z = -16
-5(2) - y + -5 = -16
-10 - y - 5 = -16
-15 - y = -16
-y = -1
y = 1