How was this Equation Solved!!!!!!!!!!!!!!!!!???

Question

Solve for y: 4x^2+9y^2=36?
The answer is y=(+/-)2√9-x^2] How was this solved?

Answer 1

You want to get y by itself.

First, let's move the 4x^2 over.

-4x^2 + 4x^2 + 9y^2 = -4x^2 + 36
0 + 9y^2 = -4x^2 + 36
9y^2 = 36 - 4x^2

Next, let's multiply both sides by (1/9) to remove the 9 from the left hand side:

(1/9)*9y^2 = (1/9)(36 - 4x^2)
1*y^2 = 36/9 - (4/9)x^2
y^2 = 4 - (4/9)x^2

Next, take the square root of both sides:

(y^2)^(1/2) = (4 - (4/9)x^2)^(1/2)
|y| = Sqrt[(4/9)(9-x^2)]
|y| = Sqrt[4/9]*Sqrt[9-x^2]
|y| = (2/3)*Sqrt[9-x^2]

Finally, get y by itself by using the definition of absolute value:

y = +/- (2/3)*Sqrt[9-x^2]

I think your answer is off by a factor of 1/3.

Answer 2

Hi,

Subtract 4x^2 from both sides. You now have:
9y^2 = 36 - 4x^2
Now divide everything by 9 and factor a 4 out of the right side. You'd have:
y^2 = 4(9 - x^2)/9
Now take the square root of both sides of the equation and put + or - in front of the radical on the right side. You get:
y = + or - square root((4(9 - x^2))/9) which simplifies to:
y = + or - 2/3 square root(9 - x^2). In your answer you missed the 3 in the denominator outside of the radical.

I hope that helps.

Answer 3

4x^2+9y^2 = 36
9y^2 = 36 - 4x^2
y^2 = 4 - 4/9x^2
y = +/- sqrt( 4 - 4/9x^2)
y = +/- 2 sqrt( 1 - 1/9x^2)

If I did this correctly then your answer is not exactly correct, but close. The sqrt must include the x^2 parameter as my answer reflects.

Answer 4

Substitute your answer into the original equation and you should get an Identity 36=36, but you don't. Your answer is incorrect.

The correct answer is y=(SQRT(36-4X^2))/3.
Make the substitution and you will get an Identity
thereby proving it all by yourself.

Answer 5

That's not a solution!
The general form of the formula is: x^2 + y^2 = r^2
It's the formula for a circle, of radius r.

Your formula becomes: (2x)^2 +(3y)^2 = 6^2
It's a distorted circle (ellipse), of radius 6.

Answer 6

well when i tried solving it i got y=-2/3x + 2 but hey i dont know.

Answer 7

there were just finding the answer in terms of y...so they moved everything to the other side to get y by itself....the last step they did was get rid of the exponent of y