anonymous
  • anonymous
Solve the systems using substitution. 6x + 2y = 0 4x + y = -1 3x + 2y = -4 x + 2y = -8 5x - 4y = 14 x - 2y = -2 x + 3y = -4 4x + 5y = 5 x + 3y = -5 2x - y = 18
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmale
  • mathmale
One problem per post, please. Which one will it be for this post?
anonymous
  • anonymous
6x + 2y = 0 4x + y = -1
mathmale
  • mathmale
You are to use the subst. method. Choose one of these 2 equations and solve it for y. Which equation would you choose for this, and why?

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anonymous
  • anonymous
6x + 2y = 0 This one seems a bit more simpler
mathmale
  • mathmale
OK. But I'd choose the 2nd one, because solving for y is easier than solving an equation in 2y for y. so: Let's solve 6x+2y=0 for y. Start by dividing all 3 terms by what number?
anonymous
  • anonymous
6? That or zero.
mathmale
  • mathmale
Can't divide by zero, so zero is out. I'd suggested that we solve the 1st equation for y. That means focusing on the y term, not the x term. Divide all 3 coefficients of your equation by 2. What do you obtain?
anonymous
  • anonymous
3x+y=0
mathmale
  • mathmale
Good. Now, please solve that resulting equation for y.
mathmale
  • mathmale
All you have to do is to subtract 3x from both sides of the equation.
anonymous
  • anonymous
So subtract 3x from 3x and 0?
mathmale
  • mathmale
Yes. 3x-3x=0;. 0-3x = -3x
mathmale
  • mathmale
What's left?
anonymous
  • anonymous
y=-3?
mathmale
  • mathmale
You have to include that ' x ' also. 3x + y = 0 -3x -3x --------------- y= ?
anonymous
  • anonymous
-3x
mathmale
  • mathmale
Better. y=-3x. what is the second equation? Type it out now, as is.
anonymous
  • anonymous
4x + y = -1
anonymous
  • anonymous
Oh wait, sorry, let me fix it
anonymous
  • anonymous
4x + -3x = -1
mathmale
  • mathmale
it's best not to write " +- " Combine these 2 signs: (-1)(1)=?
mathmale
  • mathmale
Then re-write your equation.
anonymous
  • anonymous
Im a bit confused by what your asking, really sorry
mathmale
  • mathmale
You have written 4x + -3y = -1. The " + - " is not acceptable; simplify it to just - .
anonymous
  • anonymous
Oh ok. 4x -3x = -1 like that?
mathmale
  • mathmale
Much better. Now combine the 2 x terms on the left side of your equation.
anonymous
  • anonymous
-1x=-1
mathmale
  • mathmale
But isn't 4x - 3x = +x ?
anonymous
  • anonymous
so.... -1x=x? Im sorry this is taking so long, I got really nobody around to explain any of this to me
mathmale
  • mathmale
that's what I'm here for. ;) 4x - 3x = +x. Therefore your equation 4x - 3x = -1 becomes x = -1. OK with this?
anonymous
  • anonymous
Im pretty sure.
mathmale
  • mathmale
We've already found that y=-3x. To find the numerical value of y, please substitute (-1) for x in this equation and compute the value of y. y=?
anonymous
  • anonymous
-4 - 3 = +x.
anonymous
  • anonymous
Srry if thats wrong
mathmale
  • mathmale
formula for y: y=-3x. Known value for x: x=-1 substituting x=-1 into y=-3(x), y=-3(-1) = ? (Note: Multiply, not + or - )
anonymous
  • anonymous
Im getting confused :(
mathmale
  • mathmale
I'm sorry. We're going to go thru this problem again. First, let's do it a different way, that might be faster.
anonymous
  • anonymous
Ok
mathmale
  • mathmale
6x + 2y = 0 is the first equation; 4x + y = -1 is the second.
mathmale
  • mathmale
If we use the second equation instead of the first, we won't have to divde the y term by 2. The first equation has a y-term of 2y; the second equation has a y-term of just y. So, it makes sense to solve the 2nd equation for y, not the first.
anonymous
  • anonymous
Ok
mathmale
  • mathmale
If the 2nd equation is 4x + y = -1, all we have to do is to subtract 4x from both sides. Can you do that? 4x + y = -1 -4x = -4x ------------------- Please combine these equations to obtain a simpler, new one.
anonymous
  • anonymous
x+y=3x? or do we just remove that first x?
anonymous
  • anonymous
Oh wait no.
anonymous
  • anonymous
x+y=-5x
mathmale
  • mathmale
Note: 4x -4x ------ 0. Therefore, we get 4x + y = -1 -4x -4x ----------------- 0 = y = -1-4x or y= -1 -4x.
mathmale
  • mathmale
are you OK with this, or does it need further discussion?
anonymous
  • anonymous
So right now we got 0 - y = -5x?
mathmale
  • mathmale
that's 0 + y = -1 - 4x, or simply y = -1 - 4x.
mathmale
  • mathmale
The -1 and the -4x are NOT like terms, so can't be combined. -1 - 4 = -5 YES but -1 -4x is not -5x; it stays as -1 - 4x.
anonymous
  • anonymous
Oh ok. And we already know what x is from the other problem
mathmale
  • mathmale
Don't remember! We have to substitute this y = -1 -4x into the other equation, so we end up with 6x + 2 (-1-4x) = 0 which is an equation in x alone (no y). 6x - 1 - 4x = 0. OK? If not, ask questions.
anonymous
  • anonymous
Can you explain that in a bit easier way?
mathmale
  • mathmale
Sorry...I've made a number of typing mistakes which probably have made this even more difficult for you. I'd suggest we just stick with our previous solution and move on to another problem.
anonymous
  • anonymous
Oh ok. So for this problem can you paste into a reply what I put down? all these different ones are confusing me :(
mathmale
  • mathmale
We got 4x - 3x = -1, which translates into x = -1. Then, knowing that y=-3x, we got y =3. so, the solution is (-1,3). I'd love to copy and paste, but my computer is not allowing me to do so at the moment. I will go thru this problem with yo u again later if y ou like. but for now, would you please pick anotehr problem to work on? How many such problems do you have left to do?
anonymous
  • anonymous
3x + 2y = -4 x + 2y = -8 After this one I got 3 more
mathmale
  • mathmale
Look at the 2nd equation. Since the coefficient of x is 1, I think we should solve this equation for x, not the other equation. if x + 2y = -8, let's subtract 2y from both sides to isolate the y term: -2y -2y -------------- x = ??
anonymous
  • anonymous
-6y?
mathmale
  • mathmale
We have -8 - 2y on the right side. -8 and -2y are NOT "like" terms in that one has y, the other does not. Thus, we cannot combine the -8 and the 2 to get 6. Again, the final result is x= -8 - 2y. Can you accept this? If not, ask questions.
mathmale
  • mathmale
@Pingurox ?
anonymous
  • anonymous
Sorry, had to feed my dog
anonymous
  • anonymous
And yes, I can accept that
mathmale
  • mathmale
Since you can review this conversation later, please accept that x= -8 -2y. Next, we substitute this into the other equation: 3x + 2y = -4.
mathmale
  • mathmale
3( ) + 2y = -4 Please write -8-2y inside this set of parentheses.
anonymous
  • anonymous
3(-8-2y ) + 2y = -4
mathmale
  • mathmale
Yes. Good. Multiply each term -8 -2y by 3. What do you get? (Leave the other terms alone)
anonymous
  • anonymous
So multiply -8 -2y by 3 each?
mathmale
  • mathmale
Yes. that's the "Distribution Rule of Multiplication."
anonymous
  • anonymous
So I multiple them seperately or together?
mathmale
  • mathmale
Multiply the -8 by 3. Separately, multiply the -2y term by 3.
mathmale
  • mathmale
Separately. And keep the products (answers) separate.
anonymous
  • anonymous
-8 by 3.= -24 -2y by 3. =-6y
mathmale
  • mathmale
Right. So, on the left side of your equation, you have -24 - 6y +2y = -4. Combine the -6y and the -2y on the left, to form just one term with y in it.
mathmale
  • mathmale
-6y+2y = ? (note that you have 2 different signs here).
anonymous
  • anonymous
Uhh....im a wee bit lossed
mathmale
  • mathmale
-6+2=-4, so -6y+2y = -4 y. Then, on the left side y ou have -24 - 4y=-4. Adding 24 to both sides eliminates the -24 on the left and results in -4y=-4+24, or -4y=20 Can y ou now find y?
mathmale
  • mathmale
If -4y=20, divide both sides by -4.
anonymous
  • anonymous
divide -4y and 20 by -4?
mathmale
  • mathmale
Yes. -4y divided by -4 is simply y. We want y alone on the left side. So, now on the left side we have y, and on the right side we have 20 / (-4), or
mathmale
  • mathmale
\[\frac{ 20 }{ -4 }=?\]
mathmale
  • mathmale
What is 20 divided by -4?
mathmale
  • mathmale
20 divided by 4 is 5. The only thing different in our "what is 20 divided by -4" is that the 4 is negative. 20/4=5, 20 / (-4) = ??
anonymous
  • anonymous
-5
mathmale
  • mathmale
right. So, on the left of our equation we now have y and on the right side we have -5. Therefore, y = -5. You can substitute y=-5 into either of the 2 given equations to find x. suppose we choose to use the equation x+2y=-8. Substituting y = -5, x + 2(-5) = - 8 What is 2(-5), if we multiply?
anonymous
  • anonymous
-10
mathmale
  • mathmale
Yes, and so you have x - 10 = -8 and you need to add 10 to both sides to obtain a value for x. Finish this, please: x - 10 = -8 +10 = +10 ________________ x = ?
anonymous
  • anonymous
x-20=-18 Im just gueesng....x=-2?
mathmale
  • mathmale
On the right side you have -8 + 10, and that comes out to just 2. Therefore, x = 2. Earlier, we found that y =-5 Therefore your solution is (2,-5). x=2 and y=-5. These 2 equations have graphs which are straight lines. If you were to graph them you'd see that they intersect at the point (2,-5).
anonymous
  • anonymous
Alright. So just copy paste that into my worksheet for my solution?
mathmale
  • mathmale
You can do that, of course. But I'd feel better if you'd not just accept this result as our answer, but rather check it by substitution. You can substitute x=2 and y=-5 into either equation. If the equation is then true, your solution is correct; otherwise it is not correct.
mathmale
  • mathmale
I encourage you to try this! I've done it myself and find that the first equation is true when x=2 and y=-5. But it's important that y ou know how to do this for ourself.
mathmale
  • mathmale
@Pingurox: I'm sorry but my head is swimming after hours on OpenStudy. I need to get off OpenStudy. I hope you'll go through our solution of the 2nd problem again and make a list of any questions you may have about that process. We could discuss your questions later. But I have to excuse myself right now. Best of luck to you, and thanks for your persistence.
anonymous
  • anonymous
No problem. I gtg anyways
anonymous
  • anonymous
anybody still there

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