Question 123991: I have to solve each system by the addition method, and if a unique solution does not exist, state whether the system is inconsistent or dependent. I have no clue how to do these and I am hoping someone will help me.
x+2y+z=2
2x+3y+3z=-3
2x+3y+2z=2
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! x + 2y + z = 2
2x+ 3y +3z =-3
2x+ 3y +2z = 2
:
notice if you multiply the 2nd equation by -1, & add it to the 3rd equation
:
-2x - 3y -3z =+3
2x + 3y +2z = 2
------------------ adding eliminates both x & y, leaving us z
0x + 0y - 1z = 5
-z = 5
therefore
z = -5
:
Substitute -5 for z in the 1st equation
x + 2y - 5 = 2
x + 2y = 2 + 5
x + 2y = 7
:
Substitute -5 for z in the 2nd equation
2x + 3y + 3(-5) = -3
2x + 3y - 15 = -3
2x + 3y = -3 + 15
2x + 3y = +12
:
Now we can deal with 2 unknown equations to find x * y
Multiply eq: x +2y = 7 by -2 and add it to the above equation:
-2x -4y = -14
2x +3y = +12
---------------- adding eliminates x, find y
0x - 1y = -2
y = +2
:
Find x using the 2nd equation, substitute for y and z:
2x + 3y +3z =-3
2x+ 3(2) + 3(-5) = -3
2x + 6 - 15 = -3
2x - 9 = -3
2x = -3 + 9
2x = 6
x = +3
:
Check solution in the 3rd equation
2x+ 3y +2z = 2
2(3) + 3(2) +2(-5) =
6 + 6 - 10 = 2
:
Therefore we can say this system is dependent on:
x = 3
y = 2
z = -5
:
I know there are a lot steps, but none of them are complicated, try to study
the procedure until it makes sense. A
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