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solve the linear system using substitution -x+2/9y=1 9x+3y=6 this is on question that...

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lflint29 | Student, College Freshman | eNoter

Posted June 6, 2013 at 9:30 PM via web

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solve the linear system using substitution

-x+2/9y=1

9x+3y=6

this is on question that was asked ..so.im guessing after sloving it ..it would be elimination the linear system ...SOMEONE PLEASE HELPPP 

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

Posted June 7, 2013 at 1:27 AM (Answer #1)

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Solve the system `-x+2/9 y=1;9x+3y=6` :

(1) Using substitution:

Solve the first equation for x

`x=2/9y-1` Now substitute this expression in place of x in the second equation:

`9(2/9y-1)+3y=6` Then solve for y

`2y-9+3y=6`

5y=15

y=3 ==>`x=2/9(3)-1=2/3-1=-1/3`

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So the solution is `x=-1/3,y=3` or `(-1/3,3)`

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Check: `-(-1/3)+2/9(3)=1/3+2/3=1`

and `9(-1/3)+3(3)=-3+9=6`

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(2) Using combinations: write both equations in the same form

`-x+2/9y=1`
`9x+3y=6`

Multiply the first equation by 9:

`-9x+2y=9`
`9x+3y=6`    Add the two equations

5y=15 ==>y=3

Substituting y=3 into the second equation yields

9x+3(3)=6 ==>9x=-3 ==> `x=-1/3` as before.

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