Question

Solve system of equations...

Answer 1

x+y+7z =17
x+y+4z=8
x-9y+4z=28

Answer 2

please, take the first two equation, and solve them in order to find x, and y, consider z not a variable

Answer 3

That is what I did

Answer 4

x+y+7z=17 *4> -4x-4y-28z=-68
x+y+4z=8 *7> 7x+7y+28z=56

Answer 5

=3x+3y=-12

Answer 6

2 and 3:
x+y+4z=8 *-1> -x-y-4z=-8
x-9y+4z=28
=-10y=20

Answer 7

sorry take the first and the third equations I have made an error

Answer 8

you will get this system:
\[x+y=17-7z,x-9y=28-4z\]

Answer 9

x+y+7z=17 *-4> -4x-4y-28z=-68
x-9y+4z=28 *7> 7x-63+28z=196

Answer 10

now, please solve the system for x, usin, for example the substitution method,, please consider z like a known quantity

Answer 11

ok I see you moved the z instead

Answer 12

@TMA76 for example from the first equation I get:
\[x=17-7z-y\]
please insert that expression into the second equation of your system

Answer 13

I dont understand

Answer 14

x=17 -y-7z
x=8-y-4z

Answer 15

subtract equation 2 from equation 1 getting 3z = 9 solve for z, getting z = 3
subtract equation 3 from equation 2 getting 10y = -20 solve for y, getting y = -2
Substitute the solved values for z and y in any of the three equations and solve for x, getting, x = -2.

Answer 16

please, @TMA76 insert the formula 17-y-7z, into the subsequent equation:
x-9y=28-4z in place of x

Answer 17

@radar can you show me how you go that because I am so confused right now

Answer 18

ok i got it

Answer 19

you showed me different what I tried to learn from

Answer 20

Yes, it is the "elimination" process, a method that is taught to solve system of equations. Take the first line in my post above and observe the following:
x + Y +7z =17
x + y + 4z =8 subtract
-------------------
0 + 0 +3z =9 3z = 9 divide both sides by 3 and get z = 3
Did you follow the method for solving z. Note the x and y variables were "eliminated" by the subtraction......they will be solved later.....do you understand how z was solved?

Answer 21

O.K. were you asked to solve by "substitution" method? or the elimination method ?

Answer 22

solution set which is supposed to be -2,-2,3

Answer 23

but I still havent solved x by plugging y or z. I think you are doing it reverse.

Answer 24

instead I got 6 for x instead of -2

Answer 25

To verify your value of 6, substitute it in equation 1, with the values you've obtained for z and y. Here is what it got, my solution set was (-2. -2. 3)
x+y + 7z = 17
-2 -2 +7(3) = 17
-4 + 21 = 17
17=17 As you can see it checks out correctly. Please post your work where you solved for x and obtain a 6. I will try and follow it and point out where you went astray.

Answer 26

ok i plugged y and z for the third equation but it did not work for the first one because I got 6

Answer 27

third equation i got -2 so it works

Answer 28

ok so on the first one I plug 6 back in

Answer 29

wait so I dont put y and z to equation 1 but only for equation 2 or 3?

Answer 30

3rd equation: x - 9y + 4z = 28 substituting the 3 for z and -2 for y
x -9(-2) +4(3) = 28
x + 18 + 12 = 28
x + 30 =28
x=28-30
x = -2

Answer 31

Let me understand what you have solved.........what have you solved for z? What have you solved for y?

Answer 32

z=3
y=-2
I have not figured out x
but z and y does not work for equation 1
it works for equation 3 to get x

Answer 33

If you have a value of 6 for x, it won't work out for equation 1, 2, or 3. It is simply wrong if you substitute the values you have for y and z (which are correct) you will get the correct answer for x in any of those 3 equations.

Answer 34

so I only use equation 2 or 3 and not 1?

Answer 35

plug y and z only to equation 2 or 3 and not 1

Answer 36

sorry wrong pic

Answer 37

You made an error in your solution for x in the drawing (link) When you moved the -2 to the right of the equal sign (adding 2 to both sides, you did not use a +2 on the right. Instead of 15, you should have 19.

Answer 38

Straighten out that algebra error and you will do O.K.

Answer 39

ok

Answer 40

tha nkz

Answer 41

You made a similar error on the first link when you solved for y. Hey no problem you are most welcome. If you look at my first post, you will find that the order in which I eliminated the variables was pretty efficient and simple. The order is really up to you, you can solve in any order, eliminating the variable of your choice.

Answer 42

Good luck with your studies TMA76.