Please help me figure out elimination I am so confused? Use elimination to solve the following system of equations. 4x+y+3z=0 2x-2y-z=10 3x-2y+2z=11

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Please help me figure out elimination I am so confused? Use elimination to solve the following system of equations. 4x+y+3z=0 2x-2y-z=10 3x-2y+2z=11

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videos online make no sense to me :(
these are not hard...but they are very time consuming and if you make a mistake at the beginning of the problem, it will carry through to the end and you will get it wrong...so it is also important to check your work when you are finished. first take 2 of the equations (any two) and eliminate a variable 3x - 2y + 2z = 11 ---(multiply everything by -1...we are eliminating y) 2x - 2y - z = 10 -------------- -3x + 2y - 2z = -11 (result of multiplying by -1) 2x - 2y - z = 10 ---------------add -x - 3z = -1 you understand so far ?
yes kind of. so what do i do with -x-3z=-1 ?

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like my answer has to be an ordered triple like (2,-3,4) for example?
Set that first part aside for now... now take 1 of the equations you used and the one that you haven't used yet...and eliminate y. You always have to eliminate the same variable as you did in the first part. 4x + y + 3z = 0 -- multiply by 2 2x - 2y - z = 10 -------------- 8x + 2y + 6z = 0 (result of multiplying by 2) 2x - 2y - z = 10 -------------add 10x + 5z = 10 any questions so far ?
ok so what do i do with 10x + 5z = 10 and -x - 3z = -1 ?
@texaschic101 we have two method , (method gauss ) or (method cramer) we can use to find it
?
did u study method cramer in algebra ?
i mean matrix and this things
hold on...I am not getting the right answer....let me try again 2x - 2y - z = 10 --- multiply by -1 3x - 2y + 2z = 11 --------------- -2x + 2y + z = -10 (result of multiplying by -1) 3x - 2y + 2z = 11 ---------------add x + 3z = 1 3x - 2y + 2z = 11 4x + y + 3z = 0 --- multiply by 2 --------------- 3x - 2y + 2z = 11 8x + 2y + 6z = 0 ---------------add 11x + 8z = 11 now take your results and eliminate a variable x + 3z = 1 --- multiply by -11 11x + 8z = 11 ------------ -11x - 33z = -11 11x + 8z = 11 -------------- -25z = 0 z = 0 now take one of the equations you eliminated y out of and sub in 0 for z x + 3z = 1 x + 3(0) = 1 x = 1 now take one of your original equations and sub in x and z to find y 2x - 2y - z = 10 2(1) - 2y -0 = 10 2 - 2y = 10 -2y = 10 - 2 -2y = 8 y = -4 now we check... 3x - 2y + 2z =11 3(1) - 2(-4) + 2(0) = 11 3 + 8 + 0 = 11 11 = 11 (correct) answer is (1,-4,0)
sorry about that....do you have questions ?
that explained it absolutely perfectly! thank u so much! just got a 100 on my test lol I was waiting just for that one question bc I didn't get it!
congrats on the test. This is probably not the easiest way to get the answer...I am just not too good with matrices

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