Question

How do you solve the following system: `5x+y=-7 , 12x-9y=-3`?

Answer 1

`x=-22/19`, `y=-23/19`.

Explanation:

I would recommend the method of elimination.

We have our 2 equations:

`5x+y = -7`
`12x-9y = -3`

Take the first equation and multiply it through by `9` to obtain, this will allow us to get the same number of `y`s on both equations so we can add them and eliminate as follows

`45x+9y = -63`

We can now add this to the second equation and we get:

`(12x-9y)+(45x+9y) = (-3) + (-63)`

Now, by gathering the like terms we see that `y` cancels to `0`.

`57x = -66 -> x = -66/57=-22/19`

Now that we have a value for `x` put this value into back into either of the first or second equation and solve for `y`. Here we will use the first equation and get:

`5(-22/19)+y=-7`
`-> y = 5(22/19)-7=110/19 - 133/19=-23/19`

And so we see that:

`x=-22/19`, `y=-23/19`.

As we chose the first equation to put our value of `x` into it is good practice to check these to make sure that the second equation is satisfied as well.

`12(-22/19) -9(-23/19) =-264/19+207/19=-57/19=-3`

So the second equation is also satisfied.