SOLUTION: When working with several different equations as a system such as below:
2X - Y + 4Z = -5
X + 2Y - Z = 6
X + Y + Z = 1
How many solutions are there ( none, 1, 3, or infinit
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-> SOLUTION: When working with several different equations as a system such as below:
2X - Y + 4Z = -5
X + 2Y - Z = 6
X + Y + Z = 1
How many solutions are there ( none, 1, 3, or infinit
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Question 84282: When working with several different equations as a system such as below:
2X - Y + 4Z = -5
X + 2Y - Z = 6
X + Y + Z = 1
How many solutions are there ( none, 1, 3, or infinite) Please explain.
Thanks, I am a 48 year old male returning to college math after almost 30 years and am very confused right now...
Keith Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website! THERE SHOULD BE 3 TOTAL SOLUTION: 1 FOR X, 1 FOR Y & 1 FOR Z.
X+Y+Z=1
X+2Y-Z=6 NOW ADD THESE TWO EQUATIONS THUS:
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2X+3Y=7 NOW SUBTRACT THE FIRST EAUATION
-(2X-Y+4Z=-5)
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4Y+4Z=12 REDUCING THIS EQUATIONWE GET:
Y+Z=3 NIOW SUBSTITUTE 3 FOR (Y=Z) IN THE THIRD EQUATION THUS:
X+3=1
X=1-3
X=-2 ANSWER. NOW SUBSTITUTE -2 FOR X IN THE EQUATION 2X+3Y=7 & SOLVE FOR Y:
2*-2+3Y=7
-4+3Y=7
3Y=7+4
3Y=11
Y=11/3 ANSWER.
-2+11/3+Z=1
Z=1+2-11/3
Z=3-11/3
Z=(9-11)/3
Z=-2/3 ANSWER.
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I'LL LEAVE THE PROOF UP TO YOU. IT'S GOOD PRACTICE TO SOLVE ALL THREE EQUATIONS.
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