1
   

substitution method and linear combination method

 
 
Peg leg
 
Reply Sun 7 Nov, 2004 07:26 pm
I don't understand how to do this promblem..somebody please help!
A landscaping Company placed 2 orders with a nursery. The first order was for 13 bushes and 4 trees and totaled $487. Second order was for 6 bushed and 2 trees, and totaled $232. The bill does not list the per item price. What is the cost of one bush and one tree? Solve using Substition and Linear combination.
  • Topic Stats
  • Top Replies
  • Link to this Topic
Type: Discussion • Score: 1 • Views: 1,172 • Replies: 4
No top replies

 
SCoates
 
  1  
Reply Sun 7 Nov, 2004 07:37 pm
Well, if
6b+2t=232 and
13b+4t=487
the difference of 255$ is in 7 bushes and 2 trees.
Compare that to the price of six trees and two bushes, and you've found the price for a single bush.

Conclusion: The problem is too simple to use complex math like combi...linear...stution-whatzit.
0 Replies
 
DrewDad
 
  1  
Reply Sun 7 Nov, 2004 10:18 pm
Linear combination simply means setting up the equation in the form: 13 bushes + 4 trees = $487

Substitution means solve one equation for one variable and substitute that answer into the second equation.
0 Replies
 
markr
 
  1  
Reply Mon 8 Nov, 2004 12:37 am
"Linear combination simply means setting up the equation in the form: 6 bushes + 4 trees = $487"

That's the linear part. The combination part is when you combine them to eliminate a variable. In this case, the easiest way is to multiply the first equation by 2 to get:
12b+4t=464
13b+4t=487
then subtract the first from the second to get:
1b+0t=23 or b=23
0 Replies
 
Vengoropatubus
 
  1  
Reply Tue 9 Nov, 2004 09:12 pm
Or you could use cramer's rule. It finds where the two lines meet, and that's what you're looking for. It works like this with two equations in the form of ax+by=c
first you find the matrices which represent those equations, so you take
a[size=7]1[/size]x+b[size=7]1[/size]=c[size=7]1[/size]
a[size=7]2[/size]x+b[size=7]2[/size]=c[size=7]2[/size]
and get something like
|a[size=7]1[/size] b[size=7]1[/size]||x|_|c[size=7]1[/size]|
|a[size=7]2[/size] b[size=7]2[/size]||y|=|c[size=7]2[/size]|
then from there, you can take two different routes. You could find the inverse of the first matrice, but that would be a bit complex and probably not what you're looking for. Instead, you could use Cramer's Rule. To do this, you go
__|c[size=7]1[/size] b[size=7]1[/size]|
x=|c[size=7]2[/size] b[size=7]2[/size]|
__|a[size=7]1[/size] b[size=7]1[/size]|
__|a[size=7]2[/size] b[size=7]2[/size]|

__|a[size=7]1[/size] c[size=7]1[/size]|
y=|a[size=7]2[/size] c[size=7]2[/size]|
__|a[size=7]1[/size] b[size=7]1[/size]|
__|a[size=7]2[/size] b[size=7]2[/size]|
To evaluate those funky-lookin box things in the form of
__|a[size=7]1[/size] b[size=7]1[/size]|
__|a[size=7]2[/size] b[size=7]2[/size]|
you take a[size=7]1[/size]b[size=7]2[/size]-a[size=7]2[/size]b[size=7]1[/size]
so that's how you do it. applying it to this problem, we go
6b+2t=232
13b+4t=487
__|6_ 232|
x=|13 487|
__|6 _2|
__|13 4|

__|232_2|
y=|487 4|
__|6 _2|
__|13 4|
giving x= -354/-2 = 177 and y=-46/-2 = 23
Keep in mind that this is a lot more work than it's worth at this point. With only those 2 terms, it takes a while, but it's worth knowing for solving equations with higher numbers of variables, and of course, it changes a little bit with every extra variable. Man, if anyone wants to quote that to check out how much html that was, be my guest. And also, those little white lines are meant to be spaces as i haven't learned how to do invisitext yet and the spaces wouldn't stack up at all.
0 Replies
 
 

Related Topics

Evolution 101 - Discussion by gungasnake
Typing Equations on a PC - Discussion by Brandon9000
The Future of Artificial Intelligence - Discussion by Brandon9000
The well known Mind vs Brain. - Discussion by crayon851
Scientists Offer Proof of 'Dark Matter' - Discussion by oralloy
Blue Saturn - Discussion by oralloy
Bald Eagle-DDT Myth Still Flying High - Discussion by gungasnake
DDT: A Weapon of Mass Survival - Discussion by gungasnake
 
  1. Forums
  2. » substitution method and linear combination method
Copyright © 2025 MadLab, LLC :: Terms of Service :: Privacy Policy :: Page generated in 0.03 seconds on 01/18/2025 at 01:31:39