Can't remember how to solve equation with two variables

In summary, the conversation discussed solving an equation with two variables and the use of simultaneous equations. The equation in question was 3R^2 + A*R - y*B - C*y^2 = 0, where A, B, and C are constants. It was determined that the equation cannot be solved for R or y using the quadratic formula because the variables are not proportional. Therefore, the best approach would be to come up with another equation to solve it simultaneously.
  • #1
tim9000
867
17
Umm from memory I used to use...that triangle:
1
1 1
1 2 1
1 3 3 1
Fibonachii was it? Pathetic I can't even remember the name.
To factorise...or was it expand...polynomials...anyway, I don't think that's elevant here.
My question is; I had an equation and it boild down to:
3R^2 + A*R - y*B - C*y^2 = 0

where A, B and C are constants.

Did I have to do completing the squares or some factorisation to find how R is proportional to y?

Thanks
 
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  • #2
You cannot solve a single equation with two variables, you have to have two equations but to get how one variable relates to the other, just move everything but the variable of interest to the other side of the equation by doing the appropriate add, subtract, multiply, divide.

For example, if you had Ax + By = 0, and you wanted to know how y was related to x, you would subtract off By then divide by A and get

Ax = -By

x = -(B/A)y
 
  • #3
phinds said:
You cannot solve a single equation with two variables, you have to have two equations but to get how one variable relates to the other, just move everything but the variable of interest to the other side of the equation by doing the appropriate add, subtract, multiply, divide.

For example, if you had Ax + By = 0, and you wanted to know how y was related to x, you would subtract off By then divide by A and get

Ax = -By

x = -(B/A)y
That wouldn't work in this case, the best I could do would be

3R^2 + A*R = y*B + C*y^2

isn't it?

Ah, ok, so bottom line, I need to use simultanious eqations?

Thanks
 
  • #4
tim9000 said:
That wouldn't work in this case, the best I could do would be

3R^2 + A*R = y*B + C*y^2

isn't it?
You could solve the equation above for R in terms of y, by using the Quadratic Formula. Start by moving all terms to the left side.
##3R^2 + AR - yB - Cy^2 = 0##

In the Quadratic Formula, a = 3R2, b = A, and c = -yB - Cy2.

In post #1 you said you were trying to show that R is proportional to y -- that's not the case in the equation above. If two variables are proportional, then either one is some constant multiple of the other.

tim9000 said:
Ah, ok, so bottom line, I need to use simultanious eqations?

Thanks
 
  • #5
Ah. I missed the y^2. Just use the quadratic equation, as Mark suggested.
 
  • #6
tim9000 said:
1
1 1
1 2 1
1 3 3 1
Fibonachii was it?
Pascal.
 
  • #7
tim9000 said:
1
1 1
1 2 1
1 3 3 1
Fibonachii was it?
Svein said:
Pascal.
And for the record, Fibonacci is the correct spelling, not Fibonachii. In Italian, 'c' followed immediately by 'i' or 'e' has the ch sound. If followed by 'a', 'o', or 'u', it has the k sound.
 
  • #8
Mark44 said:
And for the record, Fibonacci is the correct spelling, not Fibonachii. In Italian, 'c' followed immediately by 'i' or 'e' has the ch sound. If followed by 'a', 'o', or 'u', it has the k sound.
Aha, thanks for the tip, I'm not great with English, let alone Latin.
 
  • #9
Svein said:
Pascal.
AAH yep, that's it.
 
  • #10
Mark44 said:
You could solve the equation above for R in terms of y, by using the Quadratic Formula. Start by moving all terms to the left side.
##3R^2 + AR - yB - Cy^2 = 0##

In the Quadratic Formula, a = 3R2, b = A, and c = -yB - Cy2.

In post #1 you said you were trying to show that R is proportional to y -- that's not the case in the equation above. If two variables are proportional, then either one is some constant multiple of the other.
That would be helpful to solve for R or y using the quadratic formula.
So are you saying this relation regardless of anything, will never be proportional, and the best I can do is solving for something like this:

R = √((12(yB+Cy^2)/36)
or
R = - √((2A^2 + 12(yB+Cy^2)/36)

?
Thanks
 
  • #11
  • #12
SteamKing said:
Fibonacci is not Latin, it's Italian.

https://en.wikipedia.org/wiki/Fibonacci
Isn't Italian just modern Latin?

Would it have been ok if I had of said
'I'm not great with English, let alone Latin derivatives'? :wink:
 
  • #13
tim9000 said:
Isn't Italian just modern Latin?

No, not really. If that were true, you could say the same about French or Spanish or Portuguese, all of which derive from Latin like Italian, but are distinct from it in their own separate ways. This group of languages is called the Romance Languages, because they each derive from the language of the Romans (Latin).
 
  • #14
SteamKing said:
No, not really. If that were true, you could say the same about French or Spanish or Portuguese, all of which derive from Latin like Italian, but are distinct from it in their own separate ways. This group of languages is called the Romance Languages, because they each derive from the language of the Romans (Latin).
Ah I have heard that term actually. I wonder when at what point each started to diverge into what you'd distinguish as a separate entity, ah well I don't want to get too far off topic. (though I doubt there are near as many things taken from Latin verbally, discounting nouns, in French, as there would be in Italian, or even Spanish)
 
  • #15
tim9000 said:
That would be helpful to solve for R or y using the quadratic formula.
So are you saying this relation regardless of anything, will never be proportional, and the best I can do is solving for something like this:

R = √((12(yB+Cy^2)/36)
or
R = - √((2A^2 + 12(yB+Cy^2)/36)

?
Thanks
Yes, that's what I'm saying. In the equation you posted, R and y are not proportional.
 
  • #16
Mark44 said:
Yes, that's what I'm saying. In the equation you posted, R and y are not proportional.
Ok, I'll see if I can come up with another equation to solve it simultaniously.
Thank you
 
  • #17
tim9000 said:
Ah I have heard that term actually. I wonder when at what point each started to diverge into what you'd distinguish as a separate entity, ah well I don't want to get too far off topic. (though I doubt there are near as many things taken from Latin verbally, discounting nouns, in French, as there would be in Italian, or even Spanish)
I would guess that French has about as many words that are recognizably of Latin origin as Italian, Spanish, or Portuguese. Although Spanish and Italian share words that are identical or close (casa means house in Italian and Spanish, but the s is pronounced differently; cortar (Sp.) and cortare (It.) -- to cut), there are many words that are very different, due to the influence on Spanish by the Moors for 700 years.
 

1. How do I solve an equation with two variables?

Solving an equation with two variables involves isolating one variable on one side of the equation and then solving for the other variable. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division on both sides of the equation.

2. What are the steps to solve an equation with two variables?

The steps to solve an equation with two variables are as follows:
1. Identify the two variables in the equation.
2. Choose one variable to isolate on one side of the equation.
3. Use algebraic operations to manipulate the equation and isolate the chosen variable.
4. Solve for the remaining variable.
5. Check the solution by plugging in the values for both variables into the original equation.

3. Can I solve an equation with two variables using a graph?

Yes, it is possible to solve an equation with two variables using a graph. First, plot the equation as a line on a coordinate plane. Then, find the point of intersection between the line and the x-axis or y-axis. This point represents the solution to the equation.

4. What should I do if I get a negative solution when solving an equation with two variables?

If you get a negative solution when solving an equation with two variables, it is important to check your work and make sure there are no mistakes. If your work is correct, it is possible that the negative solution is a valid answer to the equation. However, if the equation is representing a real-world problem, it is important to consider if the negative solution makes sense in the given context.

5. Are there any shortcuts for solving equations with two variables?

There are no specific shortcuts for solving equations with two variables, but there are strategies that can make the process easier. These include choosing to isolate the variable with the simpler coefficient, using substitution to solve for one variable in terms of the other, or using the elimination method when dealing with a system of equations.

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