Question

A) 7x-5y+4z-9=0
-x+3y+5z-2=0
5x+y+14z-20=0

b) 7x-5y+4z-9=0
-5x+4y+z-3=0
x+2y-z+1=0

c) -3x+2y-z+10=0
6x-4y+2z-10=0
5x+7y+9z-14=0

d) 5x-9y+2z-3=0
4x+2y-3z+4=0
9x-7y-z+1=0

Answer 1

Solve each system of equations please help!

Answer 2

Well first for each system you need to move the numbers with no base to the right side. So for A the equations become :
7x-5y+4z=9
-x+3y+5z=2 and
5x+y+14z=20. Do that for every single equation for B, C, and D

Answer 3

okay, done and after that?

Answer 4

Well the easiest method for me is the elimination method. I'll show you how to do it for A then you can try for B, C, and D. Since you now have your new equations you have to change the equations to try and cross out factors to keep solving for one. So for A...
you can multiply the first equation by -4 and the second by 5 so the two become 5(7x-5y+4z=9) and the second -4(-x+3y+5z=2). The goal is to keep eliminating terms that are opposite to each other. The first equation becomes 35x-25y+20z=45 and the second equation becomes 4x-12y-20z=-8. Now if you line them up you see you have opposite terms of -20z and 20z so you cross those out and add the rest

Answer 5

So after adding them it becomes 39x-37y=37. Now keep that equation to the side. After that you need to eleminate z with the last equation and one from above. So I wasn't paying attention to the fact that the last equation has 14, so we'll have some big numbers for awhile but nothing too bad

Answer 6

So if you use the first and last equation you can cross out z by making it 28z and -28z. So the first equation would have to be multiplied by 7 so it's 7(7x-5y+4z=9) and the third equation -2(5x+y+14z=20). So the first equation becomes 49x-35y+28z=63 and the last equation becomes -10x-2y-28z=-40. So you can cross out the z's and add the two equations together so that they become 39x-35y=23.

Answer 7

OK. So now you take your other simplified expression and you like terms between 39x-37y=37 and 39x-35y=23. As you can see both have 39x so you can just multiply one of them by -1 so if you do the first one it just becomes -39x+37y=-37 and you cross out the 39x because now one is - and one is +. All you have left is the y's so you add those equations for it to become 37y=-37 plus -35y=23. Added together that is 2y=-14 and if you divide -14 by 2 it is -7 so now you know that y=-7

Answer 8

yup

Answer 9

I gotta go by all you gotta do now is fill in -7 for 2 original equations and then once you get rid of the y and you have the x and z's and then you just make them have the same numbers with the same base but make sure one of them is negative, then you cross them out and solve for either x or z. Once you do that you will have the term for either x or z and y. Once you have what 2 of them equal you just fill it into any of the original equations(by original I mean when you had =9 and =2 and =20 NOT =0) and then you will have only one variable and you move the numbers without variables to the other side, then solve for the variable that's left by dividing the added numbers. Say that z=1(idk if it does) so you take it for the middle equation and put -x+3(-7)+5(1)=2. So you get -x-21+5=2, you would add 21to 2 to get 23 then subtract 5 to get 18 so it would be -x=18, then you divide by -1 and find x=-18

Answer 10

It sounds really hard but i would get someone to explain it to you in person because it's so much easier in person since you can do the straight work instead of all this reading

Answer 11

Thank you so much! I truely appreciate this!

Answer 12

I got x=-281.1 for A, is that correct?