Question

How do you solve the following system?: `3x -9y =-13 , -2x +17y = 8`

Answer 1

`x=-139/69`
`y = 50/69`

Explanation:

`3x-9y = -13` and
`-2x+17y = 8`

multiply first statement by "2" and the second statement by "3" to get to a common coefficient of 'x'
`2(3x-9y) = 2(-13)`
`3(2x+17y) = 3(8)`

`6x-18y = -26`
`6x+51y = 24`

then, subtract second statement from first statement
`-69y = -50`

now that y is isolated, we know that
`y = 50/69`

to solve for x, substitute the value for 'y' into one of the statements

`3x-9(50/69) = -13`

divide the statement by 3
`x-3(50/69)=-13/3`
`x-(50/23)=-13/3`
`x=-13/3 +50/23`

lastly, solve for lowest common denominator
`x=(-299 + 150)/69=-139/69`