SOLUTION: The question is to solve each system. If there is no solution or if there are infintely many solutions and a system's equations are dependent so state. You have to solve the system

Question 104519This question is from textbook Introductory & Intermediate Alegbra
: The question is to solve each system. If there is no solution or if there are infintely many solutions and a system's equations are dependent so state. You have to solve the system in Three Variables but I have no clue how. The question is
x+y+2z=11
x+y+3z=14
x+2y+3z=5
This question is from textbook Introductory & Intermediate Alegbra

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
x + y + 2z = 11
x + y + 3z = 14
x +2y + 3z = 5
:
Look at it; you can see that subtracting the 1st eq from the 2nd, you eliminate x & y making it easy to solve for y:
x + y + 3z = 14
x + y + 2z = 11
------------------ Subtracting eliminates x & y
0 + 0 + 1z = 3
z = 3
:
Substitute 3 for z in the 2nd and 3rd equations:
2nd equation:
x + y + 3(3) = 14
x + y + 9 = 14
x + y = 14 - 9
x + y = 5
:
3rd equation
x + 2y + 3(3) = 5
x + 2y + 9 = 5
x + 2y = 5 - 9
x + 2y = -4
:
Using these two unknown equations:
x + 2y = -4
x + y = 5
------------subtracting eliminates x
0 + 1y = -9
y = -9
:
Find x using the equation x + y = 5
x - 9 = 5
x = 5 + 9
x = 14
:
We have x = 14; y = -9; z = 3
:
Check solution in the 1st equation: x + y + 2z = 11
14 - 9 + 2(3) =
14 - 9 + 6 = 11
:
Did this give you a clue, at least?

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