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Solve for x and y using  x + 2y = 8 and 3x + 4y = 16  

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timw996 | Student, Grade 10 | Salutatorian

Posted October 25, 2010 at 11:03 PM via web

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Solve for x and y using  x + 2y = 8 and 3x + 4y = 16

 

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4 Answers | Add Yours

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Jyotsana | Student , Grade 10 | eNoter

Posted February 1, 2014 at 11:06 PM (Answer #4)

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x+2y=8

x+2y-2y=8-2y

x=8-2y

3x+4y=16

3(8-2y)+4y=16

24-6y+4y=16

24-6y+4y-24=16-24

-6y+4y=-8

-2y=-8

-2y/-2=-8/-2

y=4

x+2(4)=8

x+8=8

x+8-8=8-8

x=0

So the answer for x=0 and y=4

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william1941 | College Teacher | Valedictorian

Posted October 25, 2010 at 11:03 PM (Answer #1)

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We have the equations

x + 2y = 8 … (1)

3x + 4y = 16… (2)

Now we have to use (1) and (2) to find the value of x and y.

First use (2) – 2*(1)

=> 3x + 4y – 2*( x + 2y) = 16 – 2*8

=> 3x + 4y – 2x – 4y = 16 – 16 = 0

=> x = 0

Substitute x = 0 in (1)

=> 0 + 2y = 8

=> y = 8/2

=> y = 4

Therefore x = 0 and y = 4

The required solution is x = 0 and y = 4.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted October 25, 2010 at 11:16 PM (Answer #2)

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x+ 2y = 8........(1)

3x + 4y = 16........(2)

Let us use the elimination method to solve:

We'll multiply (1) by -2 and add to (2):

-2x - 4y = -16

3x + 4y = 16

==> Now add both equations:

==> x = 0

Now to find y , we will substitute with (1):

x + 2y = 8

0 + 2y = 8

==> 2y= 8

==> y= 4

Then, the solution is:

(x, y) = ( 0, 4)

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neela | High School Teacher | Valedictorian

Posted October 25, 2010 at 11:31 PM (Answer #3)

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x+2y = 8 .... (1).

3x+4y = 16..(2).

From (1) : 2y = 8-x. Or y = (8-x)/2.

We put y = (8-x)/2 in the second eq: 3x+y = 16.

3x+4(8-x)/2 = 16.

Multoiply by 2:

6x+4(8-x) = 2*16 = 32.

6x+32-4x = 32

6x-4x = 32-32 = 0

2x = 0

x = 0.

Put x= 0 in first equation x+2y = 8.

0+2y = 8

2y = 8

y = 8/2 = 4.

Therefore x = 0 and y = 4 are the solutions.

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