SOLUTION: I would appreciate any help with this. I don't know how to isolate the variable or which equation to work with first... Solve: 5x-2y+2z=-24 x-3y-4z=33 3x+3y-2z=7

Question 89175: I would appreciate any help with this. I don't know how to isolate the variable or which equation to work with first...
Solve:
5x-2y+2z=-24
x-3y-4z=33
3x+3y-2z=7

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve:
5x - 2y + 2z = -24
x - 3y - 4z = 33
3x + 3y - 2z = 7
:
Perform elimination operations, adding or subtracting to get rid of one of the
variables. Do this twice and you have two, 2 unknown equation which are easy to deal with.
:
There are some obvious ways you can do this in this problem to eliminate z:
Multiply the 3rd equation by -1 and Add all three.
5x - 2y + 2z = -24
x - 3y - 4z = 33
-3x - 3y + 2z = -7
---------------------adding eliminates z
3x - 8y + 0z = 2
:
Add the first & third equations:
5x - 2y + 2z = -24
3x + 3y - 2z = 7
------------------adding eliminates z again
8x + 1y = -17
:
Our two, 2 unknown equations:
3x - 8y = +2
8x + 1y = -17
:
Multiply the 2nd equation by 8 and add it to the 1st:
64x + 8y = -136
3x - 8y = +2
----------------adding eliminates y, solve for x:
67x + 0x = -134
x = -134/67
x = -2
:
Find y using 8x +y = -17
8(-2) + y = -17
-16 + y = -17
y = -17 + 16
y = -1
:
I'll let you find out what z is. Check all three solution in the original equations
RELATED QUESTIONS
2x+y=-4 x+y=-7 Find the first variable and isolate it. Then solve for that variable.... (answered by Alan3354,Theo,MathTherapy)

Struggling to help my son with this problem: I know the issue is that I cannot recall... (answered by Alan3354)

Question: Use Table A4 to compute the probability for any Normal random variable to take... (answered by CPhill)

I found where someone answered this problem...Stan H. However, I didn't understand how... (answered by stanbon)

Would you pls help me with this, I fell that is not very difficult but I don�t know what... (answered by lynnlo)

please help me with this problem & show work so that I know how to do the other problems. (answered by Cromlix)

Hi, I don't know if this equation belongs here but I would like some help with this... (answered by math_tutor2020,ikleyn)

Jaxson bought snacks for his team's practice. He bought a bag of oranges for $2.91 and a... (answered by Boreal)

I can’t find the x- and y-intercepts of this equation: {{{4y + 5x = 2y - 3x + 16}}}. I... (answered by Alan3354,MathTherapy)