Solving Linear Systems by Elimination

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October 23rd 2008, 11:59 AM
Serialkisser

Solving Linear Systems by Elimination
Edit: Sorry, just noticed it's in the wrong Categorie.

Hello, I did all this last year, but didn't memorize it (Doh) Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.
1. Solve the following linear systems of equations using substitution.
  1. y = 3x + 5
    y = 2x + 4
  2. 2x + y = 7
    4x - y = 23
2. Solve the following linear systems using elimination. Check your solutions.
  1. 3x - 2y = 18
    x + y = 16
  2. 5x + 2y = 10
    3x - 4y = -46
3. A barnyard has cows and chickens. There are 34 heads and 86 legs. If w represents the number of cows and k represents the number of chickens:
  1. Write a linear system of equations to model this situation.
  2. Solve the linear system to find the number of cows and the number of chickens in the barnyard.
  3. Verify your solution by providing a graphical solution. You can use a spreadsheet or Geometer's Sketchpad.
Sincerely,

Serialkisser
October 23rd 2008, 05:59 PM
Shyam

Reply
Quote:
Originally Posted by Serialkisser

Edit: Sorry, just noticed it's in the wrong Categorie.

Hello, I did all this last year, but didn't memorize it (Doh) Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.

Solve the following linear systems of equations using substitution.

y = 3x + 5
y = 2x + 4
Put the value of y from first equation to second

3x + 5 = 2x + 4

x = -1

y = 2

solve next question in the same way.
October 23rd 2008, 06:06 PM
Shyam
Quote:
Originally Posted by Serialkisser

Edit: Sorry, just noticed it's in the wrong Categorie.

Hello, I did all this last year, but didn't memorize it (Doh) Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.

Solve the following linear systems using elimination. Check your solutions.

3x - 2y = 18
( x + y = 16 ) . 2
Multiply second equation by 2 and add to first equation,

3x - 2y = 18
2x + 2y = 32
---------------------------
5x = 50
---------------------------
x = 10
so, y = 6

do next Ques in the same way.
October 23rd 2008, 06:27 PM
Shyam

1 Attachment(s)
Quote:
Originally Posted by Serialkisser

Edit: Sorry, just noticed it's in the wrong Categorie.

Hello, I did all this last year, but didn't memorize it (Doh) Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.

A barnyard has cows and chickens. There are 34 heads and 86 legs. If w represents the number of cows and k represents the number of chickens:

Write a linear system of equations to model this situation.
Solve the linear system to find the number of cows and the number of chickens in the barnyard.
Verify your solution by providing a graphical solution. You can use a spreadsheet or Geometer's Sketchpad.

Sincerely,

Serialkisser
Since there are 34 heads,

w + k = 34 .....................(1)

since there are 86 legs,

4w + 2k = 86 ..................(2)

Now, solve these two equations by any of the method.

See the attached graph for graphical solution (9, 25)
October 25th 2008, 09:31 AM
Serialkisser

How do I solve the word problem ? (Doh)
October 25th 2008, 05:07 PM
Serialkisser

Quote:

Originally Posted by Shyam

Put the value of y from first equation to second

3x + 5 = 2x + 4

x = -1

y = 2

solve next question in the same way.

Hmmm I tried, but got a different solution for Y

3x+5 = 2x+4

3x-2x = 4-5

-1x = 1
October 25th 2008, 05:11 PM
Shyam

Quote:

Originally Posted by Serialkisser

Hmmm I tried, but got a different solution for Y

3x+5 = 2x+4

3x-2x = 4-5

-1x = 1

so, you got

x = -1

Now, put this value of x in first equation

y= 3x + 5

y = 3(-1) +5

y = -3 + 5
y= 2

Now, you got it ???
October 25th 2008, 05:30 PM
Serialkisser

I see, but the second part ( y=2x+4) wasn't used ... why ?

U also wrote :

Quote:

Multiply second equation by 2 and add to first equation,

3x - 2y = 18
2x + 2y = 32
---------------------------
5x = 50
---------------------------
x = 10
so, y = 6

How do you know by what to multiply ?

Sorry for all that, I take online Classes :-)
October 26th 2008, 09:52 AM
Shyam
Quote:
Originally Posted by Serialkisser

Edit: Sorry, just noticed it's in the wrong Categorie.

Hello, I did all this last year, but didn't memorize it (Doh) Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.

Solve the following linear systems of equations using substitution.

2x + y = 7
4x - y = 23
from first EQN,

y = 7 - 2x

Put this value of y in second EQN,

4x - (7 - 2x) = 23

4x - 7 +2x = 23

6x = 23 + 7

x = 30/6 = 5

so, y = 7 - 2x = 7 - 2(5) = -3
October 26th 2008, 09:55 AM
Shyam

Quote:

Originally Posted by Serialkisser

I see, but the second part ( y=2x+4) wasn't used ... why ?

U also wrote :

How do you know by what to multiply ?

Sorry for all that, I take online Classes :-)

I multiplied second eqn by 2 to make the coefficients of y equal in both eqns.

go to the next page
October 26th 2008, 10:03 AM
Shyam
Quote:
Originally Posted by Serialkisser

Edit: Sorry, just noticed it's in the wrong Categorie.

Solve the following linear systems using elimination. Check your solutions.

5x + 2y = 10
3x - 4y = -46
Now, you see, in first eqn, coefficient of y is +2
and in second eqn, coefficient of y is -4
so, if you multiply first eqn by 2, the coefficient of y will be +4, and it will get cancelled by -4 of second eqn, if we add these two eqns.

so,

10x + 4y = 20
3x - 4y = -46
---------------------
13x = -26 <--------------- by adding the two eqns, (+4y and -4y get cancelled)
---------------------

x = -26/13 = -2

For calculating y, put this value of x = -2 in any of the eqn,

5(-2) + 2y = 10

-10 + 2y = 10

2y = 10 + 10

y = 20/2 = 10

Did you get it now???

Now, can you solve the Question #3, (cows and chickens) the two eqns provided by me, by elimination method??? The graph already show you the answer.
October 26th 2008, 05:28 PM
Serialkisser

Now I understand everything, thanks for your help.