Question

Solve the system by elimination:
-2x + 2y + 3z = 0
-2x - y + z =-3
2x + 3y + 3z = 5

Answer 1

Multiply the third equation by 2 and then add the equations together.
Then you'll have a two variable system, from there eliminate z or y and solve for the corresponding variable.

Answer 2

@shamil98 do you know how to find the length of the minor axis of an ellipse

Answer 3

Thanks I'll try it an report back to you if i have any problems later :)

Answer 4

I'm so confused I work it out an got z = 3/2 -3y/2

Answer 5

Is this right or wrong?

Answer 6

(1) -2x + 2y + 3z = 0

(2) -2x - y + z =-3

(3) 2x + 3y + 3z = 5

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Take equations (1) and (3) and add. This will eliminate the x terms in those two equations

(1) -2x + 2y + 3z = 0

(3) 2x + 3y + 3z = 5

-----------------------
* 5y + 6z = 5

Answer 7

Now, take equations (2) and (3) and add them. That will eliminate the x variable.

(2) -2x - y + z =-3

(3) 2x + 3y + 3z = 5

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** 2y + 4z = 2

Answer 8

Now, take the two equations that resulted from eliminating variable x in (1) and (3) and then in (2) and (3). In those two, choose eliminate variabel y OR z.

* 5y + 6z = 5

** 2y + 4z = 2

Answer 9

* 5y + 6z = 5
** 2y + 4z = 2
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Let's eliminate variable y. To do this, multiply each member of the first equation * by 2 and the second equation ** by -5.

Answer 10

z = 5/6

Answer 11

* 5y + 6z = 5 ---by 2--> 10y + 12z = 10
** 2y + 4z = 2 --> by -5 > -10y - 20z = -10
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Add ----> -8z = 0
z = 0

@Urebaa

When I multiplied equation ** by -5, I made two errors. I have corrected them here.
And, I went ahead and solved for z.

Answer 12

So, z = 0.

Answer 13

Go to equation * 5y + 6z = 5 and substitute 0 in for variable z. Then, solve for y.
Post what you get, okay?

5y + 6*0 = 5

Answer 14

5y + 0 = 5
5y = 5
y = 1

Answer 15

Yes. Now, we need the value of x.

Answer 16

Return to any one of the three original equations:

(1) -2x + 2y + 3z = 0

Substitute 0 for variable z, 1 for variable y, and solve for variable x.

(1) -2x + 2*1 + 3*0 = 0 @Urebaa Solve for x and post what you get, okay?

Answer 17

x = 1

Answer 18

Yes. The solution is (1, 1, 0). @Urebaa