Finding the X, Y, & Z?

Question

1x - 2y + 1z = -8
3x - 3y - 2z = -5
-2x - 3y + 3z = 5

Answer 1

you need to set up a matrix equation.
the rows should look like this:

1 , -2 , 1 , / -8
3 , -3 , -2 , /-5
-2 , -3 , 3 , /5

Once you set this up follow the rules of matrices to get this to a unit matrix. Once you have done this the three numbers on the right will become your answers for x, y and z. x being which ever row has the 1 in the first column. y being which ever row has the 1 in the second column. z being which ever row has the 1 in the third column.

Answer 2

I found em!

The x is after the 1, 3, and -2.
The y is after the -2, -2, and -3.
And the z is after the1, -2, and 3.

Yay me!






Ok, first, you have WAY too many letters. Your first objective is to eliminate one of them. Twice. You'll see why "twice" in a moment.

I would pick off the z's first. Look at the first and second equations. The z's would cancel if the first one were +2z instead of +1z. As such, you shoudl multiply the first equation by 2, making it

2x - 4y+ 2z = -16

Add this to the second equation, 3x - 3y - 2z = -5. The z's will cancel, and you will get a new z-less equation:

5x - 7y = -21.

Call this Equation A.

Good, the x is gone. But now I need to kill off another variable (either x or y). In order to do this, I need ANOTHER z-less equation. This is why you need to pick off the z twice, as mentioned above. Pick a different pair of equations. I would pick the first and third equations. This time, however, multiply the first equation by -3 to get

-3x + 6y - 3z = 24

Add this to the third equation, -2x - 3y + 3z = 5, and you get

-5x + 3y = 29.

Call this Equation B.


Ok, the z's have been killed (twice), and now you have equations A and B:

5x - 7y = -21
-5x + 3y = 29

Next move is to kill off one more letter. It should be clear that the x's are destineds to die right now. Add these equations together to cancel the x's and get -4y = 8. So y = -2.

Plug in this y = -2 into either Equation A or B (you don't want to use one of the original three equations yet, because if you do, you will still be stuck with two variables: y and z). If you plug y = -2 into either Equation A or B, you should get x = -7.

Now that you have x AND y, plug BOTH of these back into ANY of the original three equations to find z. You should get z = -5.

I just visually solved for x and z (y, I'm pretty sure about). Hope I'm right!

And I hope this actually HELPS you, instead of just giving you an answer.

Answer 3

Given Equations are ;
x-2y+z= -8......(1)
3x-3y-2z= -5.....(2)
-2x-3y+3z= 5.....(3)

now, equating the (2) & (3) equations we get,
3x-3y-2z= -(-2x-3y+3z)
or, 3x-3y-2z=2x+3y-3z
or, x-6y+z=0
or, x+z=6y..................(4)

now, putting the value of equation-(4) in the equation-(1) we get,
6y-2y= -8
or, 4y= -8
or, y= -2

now, putting the value of y in the (1) & (2) equation we get,
x-2(-2)+z= -8
or, x+4+z= -8
or, x+z= -12............(5) AND
3x-3(-2)-2z= -5
or, 3x+6-2z= -5
or, 3x-2z= -11...............(6)

now, from equation-(5) we get,
2x+2z= -24..............(7)

now,doing { equation(6)+equation(7) } we get,

3x-2z+2x+2z= -35
or, 5x= -35
or, x= -7

now,putting the value of x in the equation-(5) we get,
-7+z= -12
or, z= -12+7
or, z= -5

Therefore, x= -7 ; y= -2 ; z= -5 [ans.]


NOTE : You may check whether these are correct or not by putting the values of x, y & z in the given equations.

Answer 4

x=-7
y=-2
z=-5