Question

How do solve the following linear system?: `-4x + 9y = 9 , -3x + 7y= -16`?

Answer 1

`x = -207` and `y = -91`

Explanation:

We will solve this using substitution (although you can solve it with other methods, I prefer this one).

First, we must rewrite the two equations and make sure they have an identical term. I will rewrite them as follows:

`-4x + 9y = 9` will become `-12x + 27y = 27`

`-3x + 7y = -16` will become `-12x + 28y = -64`

Now as you can see, both equations now have `-12x` in common. We will use this to substitute.

We will rewrite one equation, let's use the first one, to isolate `-12x`.

`-12x + 27y = 27` will become `-12x = 27 - 27y`

Now we can substitute this into the second equation to find the first variable.

`-12x + 28y = -64`
`(27 - 27y) + 28y = -64`
`27 - 27y + 28y = -64`
`27 + y = -64`
`y = -91`

Now that we have found the value of `y`, we can move on to substitute this value to find `x`.

Take an original question, we'll use the first one, and substitute our `y` value.

`-4x + 9y = 9`
`-4x + 9 (-91) = 9`
`-4x - 819 = 9`
`-4x = 828`
`x = -207`

So now we have solved the two equations to get `y = -91` and `x = -207`.