explain how to do it
2006-12-16 05:08:28 · 10 answers · asked by criminalinvestigator23 1 in Science & Mathematics ➔ Mathematics
2x+3y+4z=y
adding -y
2x+2y+4z=0
dividing by 2
x+y+2z=0 (1)
4x+3y+4z=y
=>4x+2y+4z=0
dividing by 2
2x+y+2z=0
x+y+2z=0
subtracting
x=0
substituting
y+2z=0
y=-2z
-2z=0-8z+3z
3z=0
z=0
sub y=0
so soln set{0,0,0}
2006-12-16 05:15:57 · answer #1 · answered by raj 7 · 1⤊ 0⤋
Ok first get the y's on one side so u get
2x+2y+4z=0
4x+2y+6z=0
2x+3y+3z=0
K now apply this rule its known as the kramers rule
for x all the terms on the other side of the = are placed
x=det(0 2 4
0 2 6
0 2 3 )
/det(2 2 4
4 2 6
2 3 3)
similarly for y and z apply tht
or u can even reduce the equations
by tht x,y,z will be zer0
2006-12-16 06:11:28 · answer #2 · answered by questinme 1 · 0⤊ 0⤋
Basically your going to do the elimination method over and over again.
First pick 2 of your equations and eliminate a variable , lets eliminate y first.
2x+ 3y+4z (subtract these from each other)
4x+3y+6z
=-2x+-2z
Then pick 2 more and eliminate y again.
4x+3y+6z(4) (multiply so that the Y is the same number)
.2x+4y+3z(3)
16x+12y+24z (now subtract again to eliminate y)
6x+12y+12z
=10x+12z
Now use the 2 equations you just got to solve for x and z
-2x+-2z (-5)
10x+12z
10x+10z (subtract)
10x+12z
z=-2
Now plug your z into one of the equations,
10x=10(-2)
10x=-20
divide each side by 10
x=-2
Now use any of the three equations you were given as your question and plug in your z and x values to solve for y
2x+3y=4z
2(-2)+3y+4(-2)
-4+3y+-8
now add -4 and -8 together
-12=3y
now divide both sides by 3 to get your y value,
-12/3=-4
Your answers should be,
x=-2
y=-4
z=-2
2006-12-16 07:14:47 · answer #3 · answered by Physics 101 1 · 0⤊ 0⤋
Two ways. One by substitution, the other by matrix row reduction. To solve by substitution, set them equal to each other (since they're all stated in terms of y) and reduce. This method is very tedious and iffy. The other method is by matrices. First, set each equation equal to zero by subtracting y from each side. So you get:
0 = 2x + 2y + 4z
0 = 4x + 2y + 6z
0 = 2x + 3y + 3z
Now make a matrix of the coefficients and you get
2 2 4 | 0
4 2 6 | 0
2 3 3 | 0
Next, do row operations till you get the matrix upper triangular or lower triangular, and read the answers from the right column. I hesitate to go into this part of it, since it's a fair amount of work and I don't know if you're required to solve it this way, or the other way, by substitution, but if you need more details, email me.
2006-12-16 05:20:23 · answer #4 · answered by Joni DaNerd 6 · 0⤊ 0⤋
(1) y=2x+3y+4z
(2) y=4x+3y+6z
(3) y=2x+4y+3z
(4) (2)-(1): 0=2x+2z ==> x=-z
(5) (4) in (3) : y= 2x+4y-3x ==> x=3y ==> z=-3y
(5) in (1): y=2*3y+3y-4*3y => yy=6y+3y -12y ==> y=0
0!
2006-12-16 05:18:02 · answer #5 · answered by Mira 1 · 1⤊ 0⤋
u have homework thats funny for 2 reasons 1 schools out for christmas and 2 its the weekend.
2006-12-16 05:14:40 · answer #6 · answered by Anonymous · 1⤊ 0⤋
There are several ways. If you want to take up a butt-load of paper, you could do substitution or elimination. However, I would suggest using Cramer's Rule for this one, if you know it.
2006-12-16 07:07:21 · answer #7 · answered by booda2009 5 · 0⤊ 0⤋
I think you need to retype this problem. Otherwise, I would be able to help you with this problem.
2006-12-16 05:12:34 · answer #8 · answered by Anonymous · 0⤊ 0⤋
first find all the variables then solve
2006-12-16 05:16:58 · answer #9 · answered by Ash 2 · 1⤊ 0⤋
Do your own homework.
2006-12-16 05:09:33 · answer #10 · answered by My Evil Twin 7 · 1⤊ 0⤋