Solve for x and y using the addition method. A) x+6y= -1  -2x-8y=4         B) 3x-y= -8   -9x+2y=18

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Care to only ask 1 question at a time in terms of eNotes rules. Either post your other question separately or follow the same principles as we are about to use in this question:

  1. `x+6y = -1`
  2. `-2x -8y = 4`

Because we have 2 unknowns (x and y) we need to eliminate one of them. So multiply 1. above by 2

   3.   `2x + 12y = -2`  now add 2. to 3.

This works because  when we add `-2x + 2x` we get 0 so we are left with `-8y+12y = 4+(-2)`

`therefore 4y = 2`

`therefore y = 2/4`

`therefore y = 1/2`

Now we can substitute to find x (into the easiest equation)

`therefore x + 6y = -1` becomes

`x+6(1/2) = -1`

`therefore x = -1 - 3`

`therefore x = -4`  and we know that `y=1/2`

The solution is (-4 ; 1/2)

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