Question

How do solve the following linear system?: `-4x-15y=-1 , -3x+7y=-1`?

Answer 1

The same values of `x` and `y` must satisfy both equations

Explanation:

Probably the easiest way to solve this is to manipulate the equations to bring them to a more convenient form in which both have the same coefficient for `x`. Multiply the fist one by `3` and the second one by `4`:

`-12x-45y=-3`
`-12x+28y=-4`

This system is equivalent to the given one. Now we subtract the second form the first, and we get:
`-73y=1`, and then `y=-1/73`. Now replacing the `y` value in either equation, say the first one, we have:

`-12x-45*1/73=-3`, so

`-12x=-3+45/73` so

`-12x=(-219+45)/73`, and then

`-12x=-174/73`, and this results in

`x=(-1/12) * (-174/73)`, and simplifying

`x=29/146`