Can you help me solve this system of equations using elimination? 3x-2y=2 5x-5y=10

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Solve the system using elimination.

i.)  `3x - 2y = 2`

ii.)  `5x - 5y = 10`

Since equation ii) can be simplified by dividing every term by 5 this gives:

ii.)  `x - y = 2`

Multiply equation `ii.)` by -2 to get:

`-2 (x - y = 2) => -2x + 2y = -4`

Now add equation i.) and ii.) together:

`3x - 2y = 2`

`-2x + 2y = -4`

This gives:  `x = -2`

Substitute x = -2 into one of the original equations to find y.

`3x - 2y = 2`

`3(-2) - 2y = 2`

`-6 - 2y = 2`

`-2y = 8`

`y = -4`

The solution to the system is (-2, -4).

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