Question

How do you solve this system of equations: `x+ 3y = - 3 and 4x + 11y = - 14`?

Answer 1

`x=-9, y=2`

Explanation:

Let's choose a variable to cancel out. For this one, I'll choose `x`. You find the LCM of the coefficients of that variable (you want the same amount of `x` in each equation so that you can subtract and get rid of it). The LCM of `1` and `4` is `4`, so I'll multiply the first equation by `4` on both sides (if I only did one side, the equation wouldn't be equal anymore).

`4*(x+3y)=4*(-3)`

`4x+12y=-12`

Now, I can subtract the second equation from the first equation (or the first from the second. Either works.)

`(4x+12y)-(4x+11y)=(-12)-(-14)`

`4x+12y-4x-11y=-12+14`

`4x-4x+12y-11y=2`

`y=2`

Knowing this, I can plug into any equation to get the value of `x`.

`x+3(2)=-3`

`x+6=-3`

`x=-3-6`

`x=-9`

We can check these values in our other equation just be sure they're correct:

`4(-9)+11(2)=-14`

`-36+22=-14`

`-14=-14`

Since we got what we were looking for, our values are correct.