Question

teach me on how to get the value of this 3 variables
I have slight knowledge about this but i can't get the value with these systems of linear equations

help me please

Please answer clearly and explain the solution clearly and easy to understand. Thanks!
(guaranteed medal for a good answer)

Answer 1

2x+3y-z=4
3x-4y+4z=11
5x-2y+z=5

Answer 2

let's cancel a variable

Answer 3

Setup the augmented matrix:
\[\left[\begin{matrix}2 & 3 & -1 & 4 \\ 3 & -4 & 4 & 11 \\ 5 & -2 & 1 & 5\end{matrix}\right]\]

Perform row reduction (gaussian elimination): http://en.wikipedia.org/wiki/Gaussian_elimination
Add -3/2 times row 1 to row 2.
Add -5/2 times row 1 to row 3.
Add -19/17 times row 2 to row 3.
Scale row 3 by -17/45.
Add -11/2 times row 3 to row 2.
Add 1 times row 3 to row 1.
Scale row 2 by -2/17.
Add -3 times row 2 to row 1.
Scale row 1 by 1/2.

Result:
\[\left[\begin{matrix}1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 4\end{matrix}\right]\]
x = 1
y = 2
z = 4

Answer 4

could you use the long method? because i think matrices are confusing

Answer 5

Let's cancel z

Answer 6

yup

Answer 7

then?

Answer 8

Add -3/2 times equation 1 to equation 2.
Add -5/2 times equation 1 to equation 3.
Add -19/17 times equation 2 to equation 3.
Multiply both sides of equation 3 by -17/45.
Add -11/2 times equation 3 to equation 2.
Add 1 times equation 3 to equation 1.
Multiply both sides of equation 2 by -2/17.
Add -3 times equation 2 to equation 1.
Multiply both sides of equation 1 by 1/2.

Answer 9

2x+3y-z=4 z = 2x+3y-4 --(1)
3x-4y+4z=11 => 3x-4y+4z=11 --(2)
5x-2y+z=5 5x-2y+z=5 --(3)
Sub(1) into (2) and (3) respectively
3x-4y+4(2x+3y-4)=11 =>11x+8y -16 =11
5x-2y+(2x+3y-4)=5 7x+y-4 =5

11x+8y =27 –-(4)
y =9-7x –-(5)
Sub. (5) into (4)
11x+8(9-7x) =27 => -45x=-45 => x=1
Sub x=1 into (5)
y =9-7(1) = 2
Sub x=1 and y=2 into (1)
z = 2(1)+3(2)-4 =4
so x=1, y=2 , z=4

Answer 10

2x+3y-z=4
3x-4y+4z=11
5x-2y+z=5
Multiply 1st equation by 4, third by -4, and add canceling z
-3x+6y=9
can be simplified into
-x+2y=3
2y=x+3

Plug that back into equation
5x-2y+z=5
5x-(x+3)+z=5
4x-3+z=5
4x+z=8

3x-4y+4z=11
3x-2(x+3)+z=11
3x-2x+6+z=11
x+z=5

4x+z=8
x+z=5

Multiply second equ by -1 and add two equation
3x=3
x=1

x+z=5
1+z=5
z=4

let's find y using this equation from above
2y=x+3
2y=1+3
2y=4
y=2

Answer 11

i'll try to work this in a paper

Answer 12

confusing

Answer 13

step by step please

Answer 14

Try my way, it includes pretty much every steps

Answer 15

it confused me

Answer 16

lol, it takes much more time.If you know how to solve system of equations in 2 unknowns. then it's easier. In this case just make one of the variable in the equation as the subject and sub into other equations. then you'll get 2 equations in 2 unknowns then solve them

Answer 17

i know how to solve 2 unknowns

Answer 18

For anything larger than a 3x3 you should really use row reduction.

Answer 19

my teacher didn't taught us that

Answer 20

if you know how to solve 2unknown in 2 equations
then, just make one of the variables into the subject.
like i have made z as teh subject and sub into teh other equations
then i get 2equations in 2unknowns
In this case you can solve it.
first solve x and y
and sub the value of x and y to solve z :)

Answer 21

sorry teh = the, typing mistakes

Answer 22

this is what i made:

2x+3y-z=4 (1)
3x-4y+4z=11 (2)
5x-2y+z=5 (3)
I multiplied eq. 1 by 4
(2x+3y-z=4)4
then added it to eq.2
8x+12y-4z=16 (1)
3x-4y+4z=11 (2)
=11x+8y=27 (4)

then i multiplied eq.3 to -4 and added to eq.2
(5x-2y +z=5)4
then added it to eq.2
3x-4y+4z=11 eq.2
-20x+8y-4z=-20 eq. 3
=-17+4y=9 (5)

then i multiplied (5) to -2
34x-8y=-18 (5)

then i added it to (4)
11x+8y=27
34x-8y=-18
= 45x=9

x=9/45

i know my answer is wrong, but where did i go wrong?

Answer 23

=-17+4y=9 (5)
it should be -9 instead of 9

Answer 24

change the value and keep your steps, then

''then i multiplied (5) to -2
34x-8y=18 (5)

then i added it to (4)
11x+8y=27
34x-8y=18
45x=45
x=1 ''

Answer 25

wow that is a simple mistake that made me a failing quiz. Signs always get me in trouble, even in my exam I got a mistake because of a wrong sign. I will be careful know with my signs. ^_^

Answer 26

Thanks!