I need help with solutions, i.e what is the solution of x + y = -4
-3x + 2y = 2

Question

I need help with solutions, i.e what is the solution of x + y = -4 
-3x + 2y = 2

austinl · Answer

Like system of equations?

$x+y=-4$
$-3x+2y=2$
Solve for x and y?

anonymous · Answer

Yes

austinl · Answer

Are you supposed to solve it with a particular method? Or can we proceed with anything?

anonymous · Answer

I think we can proceed with anything, I'm not sure. Hold on.

anonymous · Answer

Heres an example,
Equation 1
2x - 3y = -12
2(-3) - 3(2) = -12
-6 - 6 = -12
-12 = -12
TRUE

Its solving by graphing.

austinl · Answer

Ok, well for this one I would think that substitution would be the easiest route!
Take the first equation,
$x+y=-4$
and solve it for any variable. :)

anonymous · Answer

I dont understand, so what is -4?

austinl · Answer

$x+y=-4$
Now solve that equation for one variable, x or y.

Then we will plug that value into the second equation.

anonymous · Answer

but how do i know which variable to solve for?

austinl · Answer

Doesn't matter in this case, typically you want to choose the easiest one to solve for.
For this problem, it is equally easy to solve for either.

But if you had $\color{blue}{x+3x=-4}$ for example, it would be easier to solve for x.

anonymous · Answer

But which one should I solve for?

austinl · Answer

Lets just go with x, solve it for x.
$\color{red}{x}+y=-4$

anonymous · Answer

Dude I really have no idea how to do this, like, what do I even do? How do I get x alone and get rid of y. :c

austinl · Answer

If we solve $x+y=-4$ for $x$, we have $x=-y-4$

We would then plug that into the second equation.

$3x-2y=2\Rightarrow~3(-y-4)-2y=2\Rightarrow~-3y-12-2y=2$
Combine like terms,
$-5y-12=2$
$-5y=14$

$y=-\dfrac{14}{5}$

anonymous · Answer

Ok, but see this is where I get lost because I have to match it with something, and it asks me if it has a solution of (2,2) or no solution or like, a bunch of different solutions and none are the fraction.

austinl · Answer

For this question?

anonymous · Answer

Wow I think I just figured it out, I think i have to do it on a graph..

austinl · Answer

o.m.g.... I am an idiot.
Made a typo.

austinl · Answer

$3x\color{red}{+}2y=2$

austinl · Answer

$3(-y-4)+2y=2$
$-3y-12+2y=2\Rightarrow~-y=14$
$y=-14$

austinl · Answer

Then you plug that into the equation we made for x.
$x=-y-4$
$x=-(-14)-4\Rightarrow~x=14-4=10$

austinl · Answer

@harvardgirl95 does this make sense?

austinl · Answer

Well, I have to go. Hope that made sense!