Question

How do you solve the system of equations `2x + 6y = 6` and `3x - 2y = 20`?

Answer 1

`x=6` and `y=-1`
Solve the system of equation by elimination

Explanation:

Given
`2x+6y=6` let this be 1st equation
`3x-2y=20` let this be 2nd equation

Eliminate `y`. but first, multiply all terms of 2nd equation by 3

so that it becomes

`9x-6y=60` add to the 1st equation
`2x+6y=6`
~~~~~~~~~~~~~~~
`11x+0=66` the result

`11x=66` simplify

`(11x)/11=66/11` divide both sides by 11

`x=6`

Use now the original 2nd equation and `x=6` to solve for `y`
`3x-2y=20`
`3(6)-2y=20`
`18-2y=20`
`-2y=20-18`
`-2y=2`
`(-2y)/(-2)=2/(-2)`

`(cancel(-2)y)/cancel(-2)=2/(-2)`

`y=-1`

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