Question

How am I supposed to find the solution for this system?
4x+2y+z=10
-6x-y-5z=-34
3x+3y+6z=9

Answer 1

by any of the assorted techniques that your studies have developed

Answer 2

id start by reducing the rows

Answer 3

4x+2y+z=10
-6x-y-5z=-34
3x+3y+6z=9


4x + 2y + z = 10
6x + y + 5z = 34
x + y + 2z = 3

Answer 4

i see we can have a y solucion in terms of x and z by using the last 2

Answer 5

6x + y + 5z = 34
x + y + 2z = 3


6x + 5z = 34
x + 2z = 3

Answer 6

or forget the drama of substitution and go right for the matrix juggular

rref{{4,2,1,10},{6,1,5,34},{1,1,2,3}}

http://www.wolframalpha.com/input/?i=rref%7B%7B4%2C2%2C1%2C10%7D%2C%7B6%2C1%2C5%2C34%7D%2C%7B1%2C1%2C2%2C3%7D%7D

Answer 7

the right column produces the results

Answer 8

I need to solve with substitution or elimination

Answer 9

the matrix row reduction is defined by elementary row operations that mirror the sub/elim method

Answer 10

solve 1 equation for one variable in terms of the other 2; sub that into the other 2 equation; resolve the issue with the 2 unkown 2 variable elimination and work that back into the 1st equation

Answer 11

or define the line of intersection of the first 2 planes and then calculate where that would hit the third plane

Answer 12

I tried that. I keep getting weird numbers

Answer 13

then your algebra skills need to be honed more :)

Answer 14

I just want to see someone else's steps. I know what the answers are

Answer 15

4x + 2y + z = 10 ; z=10-4x-2y, sub it in

6x + y + 5(10-4x-2y) = 34
x + y + 2(10-4x-2y) = 3


6x + y + 50 -20x -10y = 34
x + y + 20 - 8x - 4y = 3

reduce those equations for me

Answer 16

what does that mean?

Answer 17

elimination

4x + 2y + z = 10
-6x - y - 5z = -34 -->(2)
---------------
4x + 2y + z = 10
-12x - 2y - 10z = -68 (result of multiplying by 2)
---------------add
-8x - 9z = -58

-6x - y - 5z = -34 -->(3)
3x + 3y + 6z = 9
---------------
-18x - 3y - 15z = - 102 (result of multiplying by -3)
3x + 3y + 6z = 9
----------------add
-15x - 9z = - 93

-8x - 9z = -58
-15x - 9z = -93 -->(-1)
---------------
-8x - 9z = -58
15x + 9z = 93
--------------add
7x = 35
x = 5

-8x - 9z = -58
-8(5) - 9z = -58
-40 - 9z = -58
-9z = -58 + 40
-9z = - 18
z = 2

4x + 2y + z = 10
4(5) + 2y + 2 = 10
20 + 2y + 2 = 10
22 + 2y = 10
2y = 10 - 22
2y = -12
y = -6

check...
3x + 3y + 6z = 9
3(5) + 3(-6) + 6(2) = 9
15 - 18 + 12 = 9
27 - 18 = 9
9 = 9 (correct)

x = 5, y = -6, z = 2 or (5,-6,2)

Answer 18

do you have any questions ?