Question

How do you solve the system of equations `3x + 3y = - 6` and `x + 6y = - 32`?

Answer 1

`(4,-6)`

Explanation:

First, we can simplify the first equation:

`3x+3y = -6`

`(3x)/3 + (3y)/3 = (-6)/3`

`x+y = -2`

Now, subtract the first equation from the second equation:

`color(white)"X"x+6y = -32`
`-(x+y = -2)`

`color(white)"XXX-" 5y = -30`

And solve for y:

`(5y)/5 = (-30)/5`

`y = -6`

Now that we know `y`, all we have to do is plug in `-6` for `y` and solve for `x`.

`x+y = -2`

`x-6=-2`

`color(white)"e"x = 4`

So our solution is:

`x=4,y=-6 color(white)"XX"` or `color(white)"XX" (4,-6)`

Final Answer