SOLUTION: SUBSTITUTION AND ELIMINATION
1. 2X+Y-3Z=0
2. -2X+2Y+Z=-7
3. X-4Y-3Z=7
TRYING TO SOLVE FOR X,Y,Z
TRIED ELIMINATING X BY ADDING 1&2 WHICH GAVE ME 3Y-2Z=-7 ANS. IS NOW NEW AN
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Question 121110: SUBSTITUTION AND ELIMINATION
1. 2X+Y-3Z=0
2. -2X+2Y+Z=-7
3. X-4Y-3Z=7
TRYING TO SOLVE FOR X,Y,Z
TRIED ELIMINATING X BY ADDING 1&2 WHICH GAVE ME 3Y-2Z=-7 ANS. IS NOW NEW ANS.4 THEN TRIED TO SOLVE BY ELIMINATING X AGAIN BY USING1&3 WHICH CHANGED NO.3 AFTER MULT. -2(X-4Y-3Z=7 WHICH GAVE ME -2X+4Y+6Z=-14 WHICH IN TURN GAVE ME NEW ANS.5 NOW- THIS IS WHERE I GET CONFUSED DO I SOLVE FOR EITHER Y OR Z IN NEW ANSWERS 4&5 BY FINDING NEW COMMON FACTOR, THEN SOLVING? OR DO I PLACE ANY OF THE ANSWERS INTO ANOTHER PROBLEM?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
2X+ Y-3Z =0
-2X+2Y+Z =-7
X-4Y-3Z =7
-------------------
Put #3 in the #1 position:
X-4Y-3Z =7
2X+ Y-3Z =0
-2X+2Y+Z =-7
---------------
Subtract twicd #1 from #2; Add twice #1 to #3 to get:
X-4Y-3Z =7
0+9y+3Z =-14
0-6Y-5Z = 7
-----------------
Add #3 to #2 to get:
X-4Y-3Z =7
0+3y-2Z =-7
0-6Y-5Z = 7
----------------
Add twice #2 to #3 to get:
X-4Y-3Z = 7
0+3y-2Z =-7
0+ 0-9Z =-7
----------------
Divide thru #3 by -9 to get:
X-4Y-3Z = 7
0+3y-2Z =-7
0+ 0+Z = 7/9
----------------
Substitute that value of Z into #2 to solve for Y.
Then substitute the Z value and the Y value into #1 to solve for X.
-----------------------
I get :
X = 2.0741
Y = -1.8148
Z = 0.7778= 7/9
=====================
Cheers,
Stan H.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
.(1)
.=>
(I)
..(2)
.=>
(II)
..(3)
From (I) and (II) we have:
.(I)
.substitute from (II)
.(
.
.
.
.
(III)
..(3)
..substitute from (III)
..substitute from (II)
..substitute from (III)
..
..solve for
..
.
..
..
..multiply both sides by
..
..
..
...................(III)
(II)
Check:
.(1)
.=>
.
.
.
.
.
Check second and third one too
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