Question

Use the elimination method to solve the following system of equations.

2x - y + z = -3
2x + 2y + 3z = 2
3x - 3y - z = -4

show me how that's done, please?

Answer 1

I am solving it, i will attach it as a word document.

Answer 2

Alright, thank you ^^

Answer 3

Here it is, I hope this helps. Good luck!

Answer 4

tell me if you got it, I haven't attached files before.

Answer 5

Nope, I didn't get any of the files :/

Answer 6

it may take awhile

Answer 7

sorry i guess it isn't working. huh
i will try to type everything in for you. it won't be as pretty but should give you an idea.

Answer 8

So the elimination method is to have one equation of the three only have one variable; so let’s say z.I also want one equation of the three to only have 2 variables, so let’s say y and z.I will solve for this by subtracting the 2nd equation from the first, to get rid of the x variable in the 2nd equation. Set the 3rd equation aside for the moment

Answer 9

2x-y+z=-3
-(2x+2y+3z=2)
becomes
(-y-2y)+(z-3z)=(-3-2)
this is our new 2nd equation!

Answer 10

-3y-2z=-5 or this one as it has been reduced

Answer 11

I now have
2x-y+z=-3
-3y-2z=-5
3x-3y-z=-4

As you can see the first equation is still as it was, the 2nd equation now only has y and z variables. The third we will now eliminate the x and y variables to only have z.
I will take the 1st equation and subtract it from the 3rd, to get rid of the x variable in the 3rd equation.
Unfortunately this is not as easy as earlier.

Answer 12

3(2x-y+z=-3) I multiply by 3 because to eliminate the x terms there have to be equal number of x’s in each equation.
-2(3x-3y-z=-4) I multiply by -2, because I am subtracting this term from the above. If the first term was -3x I would only have to multiply by +2.

Answer 13

I now eliminate.
3(2x-y+z=-3)
-2(3x-3y-z=-4)

Answer 14

(6x-6x)+(-3y+6y)+(3z+z)=(-9+8)
This becomes 3y+4z = -1

Answer 15

Now that the third equation only has y and z terms, I will take the 2nd equation that we eliminated the x-term from and subtract the third equation that we just solved for from it.
-3y-2z=-5
3y+4z=-1

Answer 16

This looks simple. The top equation has a -3y, and the bottom a +3y, so they will eliminate with no extra work on our part. I won’t subtract the two equations from each other; I will instead add them.
(-3y+3y)+(-2z+4z)=(-5-1)
2z= -6

Answer 17

2z = -6 is the new 3rd equation!

Answer 18

So I now have 3 equations.
2x-y+z=-3
-3y-2z=-5
2z= -6

This should be considered the process of elimination. Now you have the 3rd equation where you can solve for z, than you can solve for y, by substituting that value of z into the 2nd equation, and so forth until you have all variables solved.

Answer 19

Good luck!