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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
in STEP 1, what is y-3y ??
its not y
oh i ment to type -2y i had a mess of my notes/work
ok,so u get 5x-2y=6
okay than what next
now ADD (x-2y-4z=-10) +(4x+2y+4z=10) what u get ?
oh wait, how did u get 10 ?
it shouls be 2, isn't it ?
you have to make another set of coefficients by modifying the problem so i times 2 by the equation 2x+y+2z=5
and i tryed not timeing it by two but the variables missing have to be the same in both equations
wait, where did u get 5 from ? isn't that 1 in original question ?
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
wait, i will write first 2 steps , u check
here is the example problem x + 2y – z=–3 2x – 2y + 2z = 8 2x – 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 –2y. Let’s add the first and second equations. x + 2y – z=–3 + 2x – 2y + 2z = 8 3x + 0y + z = 5 which simplifies to… 3x + z = 5 Unfortunately, you can’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 didn’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 – z = –3 x + 2y – z = –3 2(2x – y + 3z) = 9 4x – 2y + 6z = 18 Now add the two equations. x + 2y – z=–3 + 4x – 2y + 6z = 18 5x + 0y + 5z = 15 which simplifies to…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 –3x –3x z = –3x + 5 Substitute –3x + 5 for z in the equation 5x + 5z = 15 and solve for x. 5x + 5z=15 5x + 5(–3x + 5) = 15 5x – 15x + 25 = 15 –10x + 25 = 15 –25 –25 –10x = –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 –3 –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 – z=–3 (1) + 2y – (2) = –3 1 + 2y – 2 = –3 –1 + 2y = –3 +1 +1 2y = –2 y = –1 Since x = 1, y = –1 and z = 2, the solution is (1, –1, 2). Graphically, this represents the only point where the three planes intersect.
it is super confusing to me
i will write step 1 and 2 ,see whether it make sense.
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 ?
now from (2) u directly have 5x=-8 so x= -(8/5) ok ?
now since u have x, from (1) can u find y ??
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
no! in (1) u only have x and y and u got value of x..... 5x-2y=2 put x= -8/5 here ------^
oh ok so 5(-8/5)-2y=2 and y = -5
and then you would substitute those into one of the original equations right?
thats right! y=-5 :) yes, now u have x and y substitute in any of the original equation, u will get z ...
(-8/5)-2(-5)-4z=-10 i get x=22/5 is that right????
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
z is actually, 23/5=4.6 x= -8/5=-1.6 try putting -1.6,-5,4.6
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 :)))))
lol! its ok. but did u understand the process ?
yeha i mainly got confused where it said only one value in step 2 and how it was different from the example problem
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
my bad z=4
i basically just redid all the steps you shown me to finish it
okk, so the question had 2x+y+2z=10 instead of 2x+y+2z=1
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 :)
ok, but then i get the solutions as x=2 y=-0.5 z=3.25
i put 1 instead of 5 in the middle one
of the original equations
so that was a mistake on my part of typing
x=0 y=-3 z=4
yup, u are correct then
yeah thank you for helping