Rearranging Equations: 3x^2 + 2y^2 = 35

  • Thread starter Stratosphere
  • Start date
But here it is:In summary, when rearranging the given equation, 3x^2 + 2y^2 = 35, for x^2, the correct form is x^2 = -\frac{2}{3}y^2- 11\frac{2}{3} as 35/3 is equivalent to 11 and 2/3, not 11 multiplied by 2/3. Mixed numbers should be avoided for clarity.
  • #1
Stratosphere
373
0

Homework Statement



3x[tex]^{2}[/tex] + 2y[tex]^{2}[/tex] = 35

Homework Equations





The Attempt at a Solution


I rearrangged it for x[tex]^{2}[/tex] and got [tex] -\frac{2}{3}y+11\frac{2}{3}=x^{2}[/tex]
Is this right?
 
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  • #2
It looks correct to me
 
  • #3
I don't think it is 11(2/3)

[itex]3x^2 + 2y^2=35[/itex]
[itex]3x^2 = 35 - 2y^2[/itex]
[itex]x^2 = 35/3 - (2/3)y^2[/itex]

but [itex]35/3 = 11(2/3)[/itex]?
[itex]11.66.. \neq 7.33..[/itex]
 
  • #4
cshum00 said:
I don't think it is 11(2/3)

[itex]3x^2 + 2y^2=35[/itex]
[itex]3x^2 = 35 - 2y^2[/itex]
[itex]x^2 = 35/3 - (2/3)y^2[/itex]

but [itex]35/3 = 11(2/3)[/itex]?
[itex]11.66.. \neq 7.33..[/itex]

I believe [itex]11\frac{2}{3}[/itex] meant 11 and 2/3 not 11 multiplied by 2/3
 
  • #5
But it should be
[tex]x^2= -\frac{2}{3}y^2- 11\frac{2}{3}[/tex]
Not
[tex]x^2= -\frac{2}{3}y- 11 \frac{2}{3}[/tex]

I presume the missing exponent on y was a typo.
 
  • #6
rock.freak667 said:
I believe [itex]11\frac{2}{3}[/itex] meant 11 and 2/3 not 11 multiplied by 2/3

lol. Mixed numbers. It has been so long since i last used them and it should be best to be avoided.
 

FAQ: Rearranging Equations: 3x^2 + 2y^2 = 35

How do I solve for x and y in the equation 3x^2 + 2y^2 = 35?

To solve for x and y in this equation, you will need to use algebraic techniques such as factoring, substitution, or completing the square. Start by isolating one variable on one side of the equation and then solve for the other variable. Once you have one variable solved, you can plug that value into the equation to solve for the other variable.

Can I rearrange the terms in the equation 3x^2 + 2y^2 = 35 to make it easier to solve?

Yes, you can rearrange the terms in an equation as long as you do the same operation on both sides. In this case, you can rearrange the terms by moving the y^2 term to the other side of the equation and then dividing both sides by 2 to isolate the x^2 term.

What if I have multiple variables in my equation like 3x^2 + 2y^2 + 4xy = 35?

If you have multiple variables in your equation, you can still use the same techniques to solve for one variable at a time. You may need to use more advanced algebraic methods such as the quadratic formula or systems of equations to solve for all the variables.

How can I check my solution to make sure it is correct?

You can check your solution by plugging the values you found for x and y back into the original equation. If the equation is true, then your solution is correct. You can also graph the equation and see if the coordinates of your solution point lie on the graph.

Can I use a calculator to solve for x and y in this equation?

Yes, you can use a calculator to solve for x and y in this equation. However, it is important to understand the steps and methods used to solve the equation algebraically before relying on a calculator. Additionally, make sure to double check your solution using other methods to ensure accuracy.

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