Question

Help ! This makes no sense...
Solve by elimination
x + 5y - 4z = -10
2x - y + 5z = -9
2x - 10y - 5z = 0 ....

Answer 1

First, pick two equations to start with

Answer 2

The first two appears easier to me.

Multiply the first one by -2 in order to eliminate the X

Answer 3

-2x -10y +8z = -20
2x - y + 5z = -9

-9y + 13z = -29 (combine the two equations)

Now, do equation 2 and 3 : Multiply original equation 3 by -1 to eliminate the x

Answer 4

The line abve (combination) should be
-11y + 13z = -29

Answer 5

equation 2 multiplied by -1
-2x + y -5z = 9
2x - 10y -5z = 0 (orig #3)
-9y -10z = 9 combined 2 and 3

Answer 6

A. combined 1 & 2: -11y + 13z = -29
B. combined 2&3: -9y - 10z = 9
multiply A by 9
multiply B by -11

-99y + 117 z = -261
99y + 110z = -99

227z = -360
z = -360/227

Answer 7

Did you follow? Three equations are long...but has the same logic as 2 equations -

Answer 8

I'm trying to follow.. Very difficult though.

Answer 9

I know :(

Answer 10

labeled the original equations as A B C

Answer 11

It just doesn't make sense to me. lol

Answer 12

We are going to canceled out terms with equation A and B
Multiply A by -2

Combine the A' with B

Answer 13

when you combine A' and B you get -11y + 13z = -29

Answer 14

now Multp B by -1
Combine B' with C

you get -9y -10z = 9

Answer 15

combine those two and solve for Z we get -360/227
I hope my calculations were right..)

Answer 16

I almost understand. I guess I just need to read those stupid books more.

Answer 17

Now we start with -9y -10z = 9

plug in z = -360/227 and solve for Y

Answer 18

:).. let make the fraction of -360/227 a decimal = -1.59

Answer 19

I used the -9y -10z = 9 to plug for Z and solve for Y
I got Y = .76

Answer 20

now I look at original A
plug in my values for Y and Z to solve for X

Answer 21

Oh dear.. Ohkay.. Let me try lol No promises

Answer 22

I get x = -20.2

Answer 23

I can't figure it out. Plus, my calculator won't do decimals. ):

Answer 24

I am off on the Z I can't get it to check. I am still looking at it. Your calc won't decimals? strange...

Answer 25

It doesn't have the decimal point on it. It's a mini calculator

Answer 26

check out this video. same steps as I but maybe fractions work better for you
http://www.mathplanet.com/education/algebra-2/how-to-solve-system-of-linear-equations/solving-systems-of-equations-in-three-variables

Answer 27

Alrighty(:

Answer 28

Looks a little more simple. Thank you(:

Answer 29

\[\left[\begin{matrix}1 & 5 & -4 & -10 \\ 2 & -1 & 5 & -9 \\ 2 & -10 & -5 & 0 \end{matrix}\right]\]\[row_{2} += (-2)row_{1}\]\[\left[\begin{matrix}1 & 5 & -4 & -10 \\ 0 & -11 & 13 & 11 \\ 2 & -10 & -5 & 0 \end{matrix}\right]\]\[row_{3} += (-2)row_{1}\]\[\left[\begin{matrix}1 & 5 & -4 & -10 \\ 0 & -11 & 13 & 11 \\ 0 & -20 & 3 & 20 \end{matrix}\right]\]\[row_{3} += (\frac{-20}{11})row_{2}, += \frac{row_{3}}{a_{33}}\]\[\left[\begin{matrix}1 & 5 & -4 & -10 \\ 0 & -11 & 13 & 11 \\ 0 & 0 & 1 & 0 \end{matrix}\right]\]\[row_{2} += (-13)row_{3}, += (\frac{-1}{11})row_{2}\]\[\left[\begin{matrix}1 & 5 & -4 & -10 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 0 \end{matrix}\right]\]\[row_{1} += (-5)row_{2}, += (4)row_{3}\]\[\left[\begin{matrix}1 & 0 & 0 & -5 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 0 \end{matrix}\right]\]\[x= -5\]\[y= -1\]\[z= 0\]

Answer 30

THis is where i erred

when you combine A' and B you get -11y + 13z = -29

that should be -11y + 13z = 11

Answer 31

Wow... That's a lot. Thanks whoever you are. lol

Answer 32

when you combine -11y + 13z = 11
with 9 y + 10z = -9
by multiply 1st by 9 and the 2nd by 11

you get z = 0

Answer 33

from that...plug z = 0 into 9y +10z = -9

you get y = -1

Answer 34

That makes more sense. No decimals.. Thank goodness

Answer 35

plug y = -1 and z = 0 into original 1st line you get x = -5
yes matrix is a way to do this also...

Answer 36

I figured I did math error somewhere, but i found it when I went back through my steps. sorry..

Answer 37

It's fine (: that website you sent helped a lot