Homework Help

Solve the linear system of equations using substitution: `-x+2/9y=1`       ...

user profile pic

ryan133 | (Level 1) eNoter

Posted July 30, 2013 at 4:20 AM via web

dislike 1 like

Solve the linear system of equations using substitution:

`-x+2/9y=1`        `9x+3y=6`

1 Answer | Add Yours

user profile pic

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

Posted July 30, 2013 at 4:43 AM (Answer #1)

dislike 1 like

To solve using substitution, first rearrange one of the equations to reflect either x=...or y=...

`9x+3y=6`  becomes `9x=6-3y`     

`therefore x=6/9-3/9 y`

Now substitute the x value into the first equation. it is not necessary to simplify the `6/9` as it will be easier to use like that later:

`-(6/9 - 3/9 y) +2/9y = 1`  

`therefore -6/9 + 3/9 y +2/9 y = 1`  (note the symbols (-) changes)

`therefore 3/9 y + 2/9 y = 1 + 6/9`

`therefore 5/9 y = 9/9 +6/9`

`therefore 5/9 y = 15/9`

`therefore y=15/9 times 9/5`

Therefore y=3.

Now substitute into any previous equation to solve for x:

`9x +3y = 6` becomes `9x + 3(3) = 6`

`therefore 9x=6-9`

`therefore x=-3/9`

`therefore x= -1/3`

Ans: (x;y) : ( `-1/3` ; 3)

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes