Question

System of equations an example on how to do it. (Since many people here are asking similar questions, I will show you how to do at least one of these problems.) [Elimination method]

Answer 1

Oh, I was making an example. lol

Answer 2

Ex.
2x-y+4z = 17
3x+4y-z = -1
4x+3y+2z = 11

Answer 3

Finally at least someone explained!:D Thank you!!!!

Answer 4

@geekfromthefutur this noble guy is helping people learn it here

Answer 5

First thing, we'll do is label the equations to make it easier for us to know where what is.
1. 2x-y+4z=17
2. 3x+4y-z=-1
3. 4x+3y+2z=11

Now we'll pick a variable to eliminate, it's arbitrary, so with that said, lets pick z.

1. 2x-y+4z = 17
2. 3x+4y-z = -1

we want to make the variable have the same number but opposite sign, so we can eliminate it.

So we can take 2 and multiply the whole equation by 4 --> 4(3x+4y-z=-1) which would make our new equation 12x+16y-4z = -4. We will call this 2a.
Now back to 1 and 2, we can now add these equations together.

1. 2x-y+4z = 17
2a. 12x+16y-4z = -4

Adding these we get 14x+15y=13, we will call this equation 4.

4. 14x+15y=13

Now we have made an easier equation with only two variables, but to continue to eliminate one of these variables we will have to make another. So this time we'll take equations 2 and 3 and repeat the process again.

2. 3x+4y-z=-1
3. 4x+3y+2z = 11

Multiply equation 1 by 2, so 2(3x+4y-z = -1), our new equation will be 6x+8y-2z = -2 we will call this 2b.

Now we can add these two equations as before,

2b. 6x+8y-2z=-2
3. 4x+3y+2z=11

Adding these equations we get 10x+11y=9, we call this 5.

5. 10x+11y= 9

Using equations 4 and 5, we can now find the variables x and y.

4. 14x+15y=13
5. 10x+11y = 9

We'll find y first, to do this, we want to eliminate x.

Multiply equation 4 by -5 --> -5(14x+15y=13) --> -70x-75y=-65 we'll call this 4a.
Multiply equation 5 by 7 --> 7(10x+11y=9) --> 70x+77y = 63 we'll call this 5a.

Adding these two equations together

4a. 70x-75y=-65
5a. 70x +77y = 63
We get 2y = -2, dividing both sides by 2, y = -1.

Now we can pick equations 4 or 5 to substitute y in, we'll pick 5.

5. 10x+11y = 9
Substituting y = -1 we get 10x+11(-1) = 9 => x = 2.

Now we have x = 2, and y = -1, now the last part is just to find z. To do this we pick one of the original functions and substitute x = 2, and y = -1 for it. Here we'll pick equation 2 (it doesn't matter which one you pick).

2. 3x+4y-z=-1
Now we substitute the variables x and y.
3(2)+4(-1)-z = -1
6-4-z = -1
-z = -3 divide both sides by -1.
We get z = 3.


Final answer = (2,-1,3).

It looks a bit complicated but when you start doing it, you'll see it's actually very easy.

Answer 6

Just ask any questions if you don't get a specific part.

Answer 7

@CountryDoe13 @ilovehim121511 This might help you.

Answer 8

lol thank god when i used to do system of equations or whatever u call it
it wasn't this big lol

Answer 9

uh well i just remembered that i still do it in physics <.<

Answer 10

It's actually not that big haha, I was just trying to make the steps easier, by symbolizing each part, so it would be easier for the people to follow it.

Answer 11

I feel as if I need to make legit tutorials for all of high school math lol.

Answer 12

3 equations
seems pretty big
tho thank god i know this stuff >.> i'd die in physics if i didn't

Answer 13

lol go for it u r a Batmaaan
u can do it lmao
Good job tho!!!!

Answer 14

Lol, maybe later.

Answer 15

@Jaleena take a look at this
@iambatman explains it pretty good

Answer 16

Explanations *v(=u=*v) Yay

Answer 17

Who here is taking edgenuity

Answer 18

'Cause he's batman

Answer 19

elimination is similar to the matrix solution

Answer 20

Elimination is similar to shooting a deer.

Answer 21

People should first master solving two equations with two unknowns.

Then three equations with three unknowns can be reduced to two equations with two unknowns by picking one variable to eliminate between equations (1) and (2) and between (2) and (3) or (1) and (3).

Then all three unknowns can be solved.