Question

How do you solve the following system?: `-6x -3y =1, -2x +4y = -5`

Answer 1

`x =11/30,y = -16/15`

Explanation:

We have the equations:
`-6x-3y=1` and
`-2x+4y=-5`

I would say the best way to procede is to eliminate the `x` terms. Multiply the 2nd equation by 3 so that the coefficient of `x` on the 2nd equation is the same as the coefficient of `x` on the first equation giving:

That means the 2nd equation becomes:

`-6x+12y=-15`

Now subtract the equations from each other to eliminate the `x` terms and get:

`(-6x-3y)-(-6x+12y) = 1 - (-15)`
`-> -15y = 16 -> y = -16/15`

Now put this value of `y` back into either of the original equations to find `x`, we'll choose the first equation:

`-6x -3(-16/15) = 1`
`-6x +16/5 = 1`
`-> -6x = 1-16/5=-11/5`
Thus:
`x =11/30`

Hence our final solution. It is good practice to put these values into the other equation to check that they work.