Posted by Annika Rae on Sunday, January 5, 2014 at 12:18am.
1) What is the value of y in the system x+3yz=3, 6x=2y1 and x=z+3 IF x = 5/6 and z = 23/6?
2) Given the systems x+y+z=14 and 2x+y+6z=16, how many number of solutions to the system are there?

Math  Reiny, Sunday, January 5, 2014 at 10:31am
1. strange question
Without looking at your last part of the given x and z values, just solving the system ....
from the 2nd:
2y = 6x+1
y = (6x+1)/2
from the 3rd:
z = x3
back into the 1st:
x + 3y  z = 3
x + 3(6x+1)/2  (x3) = 3
times 2
2x + 18x + 3  2x + 6 = 6
18x = 15
x = 15/18 =5/6
then y = (6(5/6) + 1)/2 = 2
z = 5/6  3 = 23/6
So there is one uniques solution of (5/6, 2, 23/6)
and the value of y is 2
Now when you give an x value and a z value different from the actual solution, it will depend on which equation you sub into.
There would be 3 different answers for the value of y
2. Each equation represents a plane. Since the 2 planes are not parallel, they will intersect in a line.
There will be an infinite number of points on that line, thus there will be an infinite number of solutions for your system.
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