# Solve the linear system of equations using substitution: `-x+2/9y=1` `9x+3y=6`

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durbanville | Certified Educator

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)**

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