Question

How do you solve the system of equations `3x + 9y = 1` and `- 12x + 3y = 16`?

Answer 1

`x=-47/39` and `y=20/39`

Explanation:

Lets call `3x+9y=1` the first equation and `-12x+3y=16` the second equation.

First multiply the first equation by `4` so that it has `12` as a coefficient of the `x` term

`4xx(3x+9y)=4xx(1)`

`12x+36y=4`

Comparing to the second equation, we get

`" "12x+36y=4`
`-12x+3y=16`

Adding the two equations to each other gives

`0x+39y=20`

`39y=20`

`y=20/39`

Finally, take `y=20/39` and plug it into either of the first two original equations and solve for `x`

`3x+9color(red)(y)=1`

`3x+9(color(red)(20/39))=1`

`3x+180/39=1`

`3x=1-180/39`

`3x=39/39-180/39`

`3x=-141/39`

Dividing both sides by `3` gives

`x=-47/39`

ANSWER: `x=-47/39` and `y=20/39`