Question

How do you solve this system of equations: `-2x - y = 11 and - 2x - 9y = 3`?

Answer 1

`x = - 6`
`y = 1`

Explanation:

Solve both equations for `-2x` and set them equal to each other.

`−2x−y=11`
so `-2x = 11 + y`

`−2x−9y=3`
so `-2x = 3 + 9y`

Because both of the equations are equal to `-2x,` they are equal ro each other.

`11 + y = - 2x`   and   `-2x= 3 + 9y`

`11 + y = 3 + 9y`

1) Subtract `y` from both sides to get all the `y`'s together

`11 = 3 + 8y`

2) Subtract 3 from both sides to isolate the `8y` term

`8 = 8y`

3) Divide both sides by 8 to isolate `y`
`1 = y` `larr` answer for `y`
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To find `x`, sub in `1` for `y` and solve for `x`

`−2x−y=11`
`- 2x - 1 = 11`

1) Add 1 to both sides to isolate the `- 2x` term
`- 2x = 12`

2) Divide both sides by `- 2` to isolate `x`
`x = - 6` `larr` answer for x

Answer:
`x = - 6`
`y = 1`
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Check
Sub in the values for `x` and `y` back into the original equations.

(1) `−2x−9y=3`

`(-2)(-6) - (9)(1)` is supposed to equal `3`

`12 -9` is supposed to equal `3`

`3` does equal `3`   ✓
..................................

(2) `−2x−y=11`

`(-2)(-6) - 1` is supposed to equal `11`

`12 - 1` is supposed to equal `11`

`11` does equal `11`   ✓