SOLUTION: Solve: x-6y-2z=-8 -x+5y+3z=2 3x-2y-4z=18

Question 1014596: Solve:
x-6y-2z=-8
-x+5y+3z=2
3x-2y-4z=18

Found 2 solutions by stanbon, addingup:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve:
x-6y-2z=-8
-x+5y+3z=2
3x-2y-4z=18
---------
Add 1st row to 2nd row
Subtract 3 times 1st row from 3rd row
----------
x -6y -2z = -8
0x -y + z = -6
0x+16y+2z = 42
------
Add 16 times 2nd row to 3rd row
------
x -6y -2z = -8
0x -y + z = -6
0x +0y + 18z = -54
--------
Divide thru 3rd row by 18 to get:
x -6y -2z = -8
0x -y + z = -6
0x +0y + z = -3
------
Substitute z = -3 into 2nd row to solve for "y"::
-y -3 = -6
y = 3
----
Substitutute z = -3 and y = 3 into row 1st row to solve for "x"::
x - 6(3) -2(-3) = -8
x - 18 + 6 = -8
x - 12 = -8
x = 4
-----------
Cheers,
Stan H.
----------

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
x-6y-2z=-8
-x+5y+3z=2
3x-2y-4z=18
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x-6y-2z=-8
-x+5y+3z=2
----------
-y+z= -6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x-6y-2z=-8
3x-2y-4z=18
On the first equation multiply all terms by -3:
-3x+18y+6z= 24
Add the equations:
-3x+18y+6z= 24
3x-2y-4z= 18
---------------
16y+2z= 42
Now we have two new equations:
-y+z= -6
16y+2z= 42
Multiply the 1st equation times -2
2y-2z= 12
Add equations
16y+2z= 42
2y-2z= 12
18y= 54 Divide both sides by 18
y= 3 Now we know the value of y.
Take one of the last two equations and find z:
16y+2z= 42
16(3)+2z= 42
48+2z= 42
2z= -6
z= -3
You say, what if I chose the other equation to find z? Well:
2y-2z= 12
2(3)-2z= 12
6-2z= 12
-2z= 6
z= -3 Same answer. Cool, no?
Now we know y and z, let's go back to one of the original equations to find x:
x-6y-2z=-8
x-6(3)-2(-3)= -8
x-18+6= -8
x-12= -8
x= 4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Am I right? Let's check:
x-6y-2z=-8; 4-6(3)-2(-3)= -8; 4-18+6= 8; -18+10= -8 Correct
-x+5y+3z=2; -4+5(3)+3(-3)= 2; -4+15-9= 2; 11-9= 2 correct
3x-2y-4z=18; 3(4)-2(3)-4(-3)= 18; 12-6+12= 18; 6+12= 18 Correct
We have the correct answers.
J

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