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

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### 2 Answers

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).**

The system of equations 3x-2y=2 and 5x-5y=10 has to be solved.

3x - 2y = 2 ...(1)

5x - 5y = 10 ...(2)

In (2) cancel the number 5 common to all the terms to get the equation

x - y = 2...(3)

Now,

(1) - 3*(2) gives:

3x - 2y - 3x + 3y = 2 - 6

y = -4

(1) - 2*(2) gives:

3x - 2y - 2x + 2y = 2 - 4

x = -2

The solution of the system of equations is x = -2 and y = -4