Ok i have to solve this equation by using elimination and the steps are

- anonymous

Ok i have to solve this equation by using elimination and the steps are

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- schrodinger

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- anonymous

Step 1: Identify or Create Opposite Coefficients
Step 2: Identify or Create Opposite Coefficients AGAIN
Step 3: Solve the New System
Step 4: Substitute and Solve
I got to step number 3 and then got stuck... Here are the equations
x-2y-4z=-10
2x+y+2z=1
3x-3y-2z=1
Step 1:
(2x+y+2z=5)
+(3x-3y-2z=1)
which then equals 5x+y=6 simplified
Step 2:
x-2y-4z=-10
2(2x+y+2z=5)
(x-2y-4z=-10)
+(4x+2y+4z=10)
and then i got stuck because now there is two opposite coefficients

- hartnn

in STEP 1, what is y-3y ??

- hartnn

its not y

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- anonymous

oh i ment to type -2y i had a mess of my notes/work

- hartnn

ok,so u get 5x-2y=6

- anonymous

okay than what next

- hartnn

now ADD
(x-2y-4z=-10)
+(4x+2y+4z=10)
what u get ?

- hartnn

oh wait, how did u get 10 ?

- hartnn

it shouls be 2, isn't it ?

- hartnn

(x-2y-4z=-10)
+(4x+2y+4z=2)

- anonymous

you have to make another set of coefficients by modifying the problem so i times 2 by the equation 2x+y+2z=5

- anonymous

and i tryed not timeing it by two but the variables missing have to be the same in both equations

- hartnn

wait, where did u get 5 from ?
isn't that 1 in original question ?

- anonymous

yes because it shows that you have to like jump from step to step i included the steps up there hold on a sec i will try copying and pasting the example

- hartnn

wait, i will write first 2 steps , u check

- anonymous

here is the example problem
x + 2y â€“ z=â€“3
2x â€“ 2y + 2z = 8
2x â€“ y + 3z = 9
Step 1: Identify or Create Opposite Coefficients
Identify or create opposite coefficients in two of the equations and add them vertically. Recall that opposite coefficients allow you to eliminate variables since they have a sum of zero. Do you see any opposite coefficients? Look at the first and second equations. There is a pair of opposite coefficients in 2y and â€“2y. Letâ€™s add the first and second equations.
x + 2y â€“ z=â€“3
+ 2x â€“ 2y + 2z = 8
3x + 0y + z = 5 which simplifies toâ€¦ 3x + z = 5
Unfortunately, you canâ€™t find the value of one variable yet. Put this new equation off to the side for now, and move on to the next step.
Step 2: Identify or Create Opposite Coefficients AGAIN
This step is incredibly important! In this step, you must eliminate y again by combining two equations. But this time, you must use the equation you didnâ€™t use in step 1.
In the first and third equations, the y terms have opposite signs. So these two equations are a good choice for elimination. Multiply each term of the third equation by 2.
x + 2y â€“ z = â€“3 x + 2y â€“ z = â€“3
2(2x â€“ y + 3z) = 9 4x â€“ 2y + 6z = 18
Now add the two equations.
x + 2y â€“ z=â€“3
+ 4x â€“ 2y + 6z = 18
5x + 0y + 5z = 15 which simplifies toâ€¦5x + 5z = 15
Again, you're left with an equation with two variables instead of one. But if you go back to the new equation from Step 1, you have two equations with the same two variables. You know how to take care of that!
Step 3: Solve the New System
A new system of equations, with only two variables, has been created by eliminating y in Steps 1 and 2.
3x + z=5
5x + 5z = 15
Now this looks familiar! You can solve this system of equations using the elimination or substitution method. The substitution method looks easier since z in the first equation has a coefficient of 1. Isolate the z variable in the first equation.
3x + z =5
â€“3x â€“3x
z = â€“3x + 5
Substitute â€“3x + 5 for z in the equation 5x + 5z = 15 and solve for x.
5x + 5z=15
5x + 5(â€“3x + 5) = 15
5x â€“ 15x + 25 = 15
â€“10x + 25 = 15
â€“25 â€“25
â€“10x = â€“10
x = 1
Substitute the value of x into one of the equations and solve for z.
3x + z=5
3(1) + z = 5
3 + z = 5
â€“3 â€“3
z = 2
Now you know that x = 1 and z = 2.
Two variables down, one to go!
Step 4: Substitute and Solve
Substitute x = 1 and z = 2 into one of the original equations and solve for the remaining variable (y). Write the solution as an ordered triple. Solve for y when x = 1 and z = 2.
x + 2y â€“ z=â€“3
(1) + 2y â€“ (2) = â€“3
1 + 2y â€“ 2 = â€“3
â€“1 + 2y = â€“3
+1 +1
2y = â€“2
y = â€“1
Since x = 1, y = â€“1 and z = 2, the solution is (1, â€“1, 2).
Graphically, this represents the only point where the three planes intersect.

- anonymous

it is super confusing to me

- hartnn

i will write step 1 and 2 ,see whether it make sense.

- anonymous

oh ok

- hartnn

STEP 1:
ADD
2x+y+2z=1
+3x-3y-2z=1
__________
5x -2y +0 =2
so
5x-2y=2 ------->(1)
STEP 2:
multiply 2 to 2x+y+2z=1 ---> 4x+2y+4z=2
ADD :
x-2y-4z=-10
+4x+2y+4z=2
___________
5x +0+0=-8------>(2)
GOT THESE STEPS ?

- anonymous

yes

- hartnn

now from (2) u directly have 5x=-8
so x= -(8/5)
ok ?

- anonymous

alright

- hartnn

now since u have x, from (1) can u find y ??

- anonymous

not really i don't understand how i can get y when i only know one variable and there is three variables because in the example it shows step 2 turning into another equation

- hartnn

no! in (1) u only have x and y and u got value of x.....
5x-2y=2
put x= -8/5 here ------^

- anonymous

oh ok so 5(-8/5)-2y=2 and y = -5

- anonymous

and then you would substitute those into one of the original equations right?

- hartnn

thats right! y=-5 :)
yes, now u have x and y
substitute in any of the original equation, u will get z ...

- anonymous

(-8/5)-2(-5)-4z=-10
i get x=22/5 is that right????

- anonymous

i went to go put those into the practice and the fraction -8/5 won't even fit... im in the practice part of the lesson and i couldn't figure that out and you can put your answers in and then it will tell if it is wrong or not but i can't even put the fraction in it

- hartnn

z is actually, 23/5=4.6
x= -8/5=-1.6
try putting
-1.6,-5,4.6

- anonymous

i was on the wrong practice problem duh sorry my brain got all confused with all this thank you so much for all your help :)))))

- hartnn

lol! its ok.
but did u understand the process ?

- anonymous

yeha i mainly got confused where it said only one value in step 2 and how it was different from the example problem

- anonymous

i actually figured it out why it was wrong and not fitting in i thought i was in the wrong problem but i wasn't if you go all the way back up to step 2 where you typed it
STEP 2:
multiply 2 to 2x+y+2z=1 ---> 4x+2y+4z=2
ADD :
x-2y-4z=-10
+4x+2y+4z=2
___________
5x +0+0=-8------>(2)
the part saying 2x+y+2z=1 was supposed to be 2x+y+2z=10
and then it would simplify to 5x=0 and then x=0 and the eventually get x=0, y=-3, and then z=-4

- anonymous

my bad z=4

- anonymous

i basically just redid all the steps you shown me to finish it

- hartnn

okk, so the question had
2x+y+2z=10
instead of
2x+y+2z=1

- anonymous

yeah i think i mistyped up there so well still thanks for your help you helped me understand a lot of it so it should be good :)

- hartnn

ok, but then i get the solutions as
x=2
y=-0.5
z=3.25

- anonymous

i put 1 instead of 5 in the middle one

- anonymous

of the original equations

- anonymous

so that was a mistake on my part of typing

- hartnn

x=0
y=-3
z=4

- hartnn

yup, u are correct then

- anonymous

yeah thank you for helping

- hartnn

welcome :)

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