Solve for y: x^4 + 1/ay = xy + a.

Question

Solve for y:
x^4 + 1/ay = xy + a.

1) y = ax − 1/ ax^4 − a^2 

2) y = ax^4 − a^2/ x − 1 

3) y = ax^4 − a^2/ ax − 1 

 

4) y = x^4 − a^2/ x − 1 

5) y = ax^4 − a/ ax − 1

 

I am very confused on how to manipulate this for y because y is one both sides and I don't know what to do. Please help me! Thank you!

Answer 1

x⁴ + (1/a)y = xy + a

 

Multiply by a:  ax⁴ + y = axy + a²

 

y - axy = a² - ax⁴

 

y(1 - ax) = a² - ax⁴

 

y = (a² - ax⁴)/(1 - ax)

 

y = (ax⁴ - a²)/(ax - 1)

 

Note:  The answer choices are missing IMPORTANT parentheses!!    

 

Answer 2

You need to first move all the y terms to one side of the equation, and move all other terms to the other side of the equation.

 

 

Step one: 

Move all the y terms to the left side.  All the other terms to the right side.  When moving terms to the opposite side, always negative the signs while doing so.

 

Note, it does not necessary have to be in this order.   You could move all the y-terms to the right side of equation.

 

 

Step two:

Factor out a positive "y" using distributive property.  "y" is the common factor on the side that contains the y-terms.

 

 

Step three:

Divide both sides of the equation by the coefficients of y.  The coefficient is the value being multiplied by "y".