Question

How do you solve the following system?: `6x +5y =-1 , -5x -9y = 5`

Answer 1

`x = 16/29`
`y = -25/29`

Explanation:

For solving using substitution method you have to separate out the value of any one variable `(x or y)` in any of the equation and put it in the other equation.
Assuming `6x + 5y = -1` to be equation `1` and `-5x - 9y = 5` be equation `2`
Seperating out the value of `x`
`x = (-1 - 5y)/6` and now putting it in the second equation
`-5((-1-5y)/6) - 9y = 5`
`5((1+5y)/6) - 9y = 5`
`((5 + 25y)/6) - 9y = 5`
Now on taking `LCM` on LHS
`((5 + 25y - 54y)/6) = 5`
`(5 + 25y - 54y) = 30`
`5 - 29y = 30`
`29y = -25`
`y = -25/29`
Now put the value of `y` in any of the two equations
`(6x + 5(-25/29)) = -1`
`(6x -125/29) = -1`
`6x = 125/29 - 1`
`6x = (125-29)/29`
`6x = 96/29`
`x = 16/29`