Urgent math help (Equation related)

[CFFJR]

Kudos to you guys for giving KillerJuan a hand and teaching him how to work the problems.

Anywhere else on the web, and the best, most polite response he could have expected is a curt "do your own homework". Though cussing and insults would be more likely.

Good ol' Racketboy.

[dsheinem]

Another way to view it is that you're just using Gaussian elimination.

5x + 8y = 136 (L1)
3x + 10y = 118 (L2)

The goal is to eliminate x from the bottom equation, then y from the top equation (this generalizes for a system of n equations with n unknowns to only have the 1st term in the 1st equation, only the 2nd term in the 2nd equation, etc).

So you add -3/5 * L1 to L2. This will eliminate the x term, and it looks like this:

(-3x - 12/5y = -408/5) = L1, this is added to L2, so L2 becomes (38/5y = 182/5)

Now you eliminate the y term from L1. You multiply the new L2 by -40/38 so that it will eliminate y from the first term. So you get:

(-8y = -728/19) = L2, which is added to the original L1, so L1 becomes (5x = 1856/19).

So now your final system looks like:

5x + 0y = 1856/19
0x + 38/5y = 182/5

Solve for x and y.

I don't think you made it any easier for him

[KillerJuan77]

Ok, first of all THANK YOU!!! Second... I'm still stuck, specially on the first one:

a + n = 224
35a + 15n = 4480

I got to the part where I did this: 35(224-n)+15n=4480, then I don't really know what to do :S (Fucking ADD)

[Limewater]

Ok, first of all THANK YOU!!! Second... I'm still stuck, specially on the first one:

a + n = 224
35a + 15n = 4480

I got to the part where I did this: 35(224-n)+15n=4480, then I don't really know what to do :S (Fucking ADD)

You have 35(224 - n) + 15n = 4480.

You want to simplify the equation as much as possible, so you want to get rid of the parentheses. Think about what you can do to the equation so that you don't have to have parentheses in it anymore.

[KillerJuan77]

Ok, first of all THANK YOU!!! Second... I'm still stuck, specially on the first one:

a + n = 224
35a + 15n = 4480

I got to the part where I did this: 35(224-n)+15n=4480, then I don't really know what to do :S (Fucking ADD)

You have 35(224 - n) + 15n = 4480.

You want to simplify the equation as much as possible, so you want to get rid of the parentheses. Think about what you can do to the equation so that you don't have to have parentheses in it anymore.

So: 7840 - n + 15n = 4480 => 7840 -14n = 4480? What should I do next? Substract the 7840? Add it? I'm sorry for asking so many question but I'm terrible at math.

[J T]

Another way to view it is that you're just using Gaussian elimination.

5x + 8y = 136 (L1)
3x + 10y = 118 (L2)

The goal is to eliminate x from the bottom equation, then y from the top equation (this generalizes for a system of n equations with n unknowns to only have the 1st term in the 1st equation, only the 2nd term in the 2nd equation, etc).

So you add -3/5 * L1 to L2. This will eliminate the x term, and it looks like this:

(-3x - 12/5y = -408/5) = L1, this is added to L2, so L2 becomes (38/5y = 182/5)

Now you eliminate the y term from L1. You multiply the new L2 by -40/38 so that it will eliminate y from the first term. So you get:

(-8y = -728/19) = L2, which is added to the original L1, so L1 becomes (5x = 1856/19).

So now your final system looks like:

5x + 0y = 1856/19
0x + 38/5y = 182/5

Solve for x and y.

I agree with dsheinem, I don't think you made this any easier on him at all.

However, I've never learned Gaussian Elimination before, so it was kind of interesting to me. It doesn't seem as parsimonious to me, at least from a hand calculation standpoint. Is there any situation where Gaussian Elimination is the preferred method instead of the substitution method?

[alienjesus]

Confusing stuff

I agree with dsheinem, I don't think you made this any easier on him at all.

However, I've never learned Gaussian Elimination before, so it was kind of interesting to me. It doesn't seem as parsimonious to me, at least from a hand calculation standpoint. Is there any situation where Gaussian Elimination is the preferred method instead of the substitution method?

I have to agree, I understood everything up until this post

So: 7840 - n + 15n = 4480 => 7840 -14n = 4480? What should I do next? Substract the 7840? Add it? I'm sorry for asking so many question but I'm terrible at math.

35(224 - n) + 15n = 4480.

thats actually 7840 - 35n + 15n = 4480

so 7840 - 20n = 4480

[gtmtnbiker]

Another way to view it is that you're just using Gaussian elimination.

5x + 8y = 136 (L1)
3x + 10y = 118 (L2)

The goal is to eliminate x from the bottom equation, then y from the top equation (this generalizes for a system of n equations with n unknowns to only have the 1st term in the 1st equation, only the 2nd term in the 2nd equation, etc).

So you add -3/5 * L1 to L2. This will eliminate the x term, and it looks like this:

(-3x - 12/5y = -408/5) = L1, this is added to L2, so L2 becomes (38/5y = 182/5)

You have an error there.

It should be

(-3x -24y/5 = -408/5) = L1
L2 becomes (3x + 10y) + (-3x -24y/5) = 118 + -408/5
L2 becomes 10y - 24y/5 = 118 -408/5
Multiply everything by 5
50y - 24y = 590-408
26y = 182
y = 182/26
y = 7

Right?

[MrPopo]

Another way to view it is that you're just using Gaussian elimination.

5x + 8y = 136 (L1)
3x + 10y = 118 (L2)

The goal is to eliminate x from the bottom equation, then y from the top equation (this generalizes for a system of n equations with n unknowns to only have the 1st term in the 1st equation, only the 2nd term in the 2nd equation, etc).

So you add -3/5 * L1 to L2. This will eliminate the x term, and it looks like this:

(-3x - 12/5y = -408/5) = L1, this is added to L2, so L2 becomes (38/5y = 182/5)

Now you eliminate the y term from L1. You multiply the new L2 by -40/38 so that it will eliminate y from the first term. So you get:

(-8y = -728/19) = L2, which is added to the original L1, so L1 becomes (5x = 1856/19).

So now your final system looks like:

5x + 0y = 1856/19
0x + 38/5y = 182/5

Solve for x and y.

I agree with dsheinem, I don't think you made this any easier on him at all.

However, I've never learned Gaussian Elimination before, so it was kind of interesting to me. It doesn't seem as parsimonious to me, at least from a hand calculation standpoint. Is there any situation where Gaussian Elimination is the preferred method instead of the substitution method?

When you have three or more variables is when you really see the value. With two you can easily use substitution, but once you have three you end up doing gymnastics that are effectively equivalent to Gaussian Elimination. So in a three variable system you'd use the first equation to remove the first term from the other two, then you'd use the second (modified) equation to remove the second term from the first and third equation, then you use the third (modified) equation, which now just has the third term, and remove the third term from the first two. This leaves you with three equations that have one term each, so do the final step to solve for each term.

[pakopako]

Another way to view it is that you're just using Gaussian elimination... This will eliminate the x term, and it looks like this:

(-3x - 12/5y = -408/5) = L1, this is added to L2, so L2 becomes (38/5y = 182/5)

You have an error there. It should be:

[*](-3x -24y/5 = -408/5) = L1
[*]L2 becomes (3x + 10y) + (-3x -24y/5) = 118 + -408/5
[*]L2 becomes 10y - 24y/5 = 118 -408/5
[*]Multiply everything by 5
[*]50y - 24y = 590-408
[*]26y = 182
[*]y = 182/26
[*]y = 7

Y=7 is about all I got from that.

This is still algebra right? I still remember bits of that.

[*]5x + 8y = 136 (L1), 3x + 10y = 118 (L2)
[*]L1 - L2 = 2x -2y = 18
[*](L1 - L2) / 2 = x - y = 9
[*]x = y + 9
[*]L2 = 3(y+9) + 10y = 118
[*]L2 = 3y + 27 + 10y = 118
[*]L2 = 13y = 91
[*]L2 = y = 7

(Gah.. no "/table" BBcode here. "Bullets! Buuulleeeets!")