steve, i still have two question I don't understand.
1. x=3y-2/4,what is the value of y in terms of x ?
2. x=y^3/3y^2+y/2,what is the value of y in terms of x ?
Let's break down both questions step by step to find the value of y in terms of x.
1. x = (3y - 2) / 4
To find the value of y in terms of x, we need to isolate y on one side of the equation.
To do this, we will multiply both sides of the equation by 4 to eliminate the fraction:
4x = 3y - 2
Next, we'll simplify the equation by adding 2 to both sides:
4x + 2 = 3y
Finally, we'll divide both sides of the equation by 3 to solve for y:
(4x + 2) / 3 = y
Therefore, the value of y in terms of x is y = (4x + 2) / 3.
2. x = (y^3 / (3y^2 + y)) / 2
To find the value of y in terms of x, we'll follow a similar process.
First, let's multiply both sides of the equation by 2 to eliminate the fraction:
2x = y^3 / (3y^2 + y)
Next, let's multiply both sides of the equation by (3y^2 + y) to remove the denominator:
2x(3y^2 + y) = y^3
Now, let's distribute 2x to all terms inside the parentheses:
6yx^2 + 2xy = y^3
Next, let's subtract 2xy from both sides of the equation:
6yx^2 = y^3 - 2xy
Finally, we'll divide both sides of the equation by y to solve for y:
6x^2 = y^2 - 2x
To get y in terms of x, we'll take the square root of both sides:
√(6x^2) = √(y^2 - 2x)
Therefore, the value of y in terms of x is y = √(6x^2 + 2x).
I hope this helps clarify the process for finding the value of y in terms of x in both equations! Let me know if you have any further questions.