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 ?
Sure, I can help you with those questions. Let's solve each question step by step:
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. Here's how you can do it:
- Multiply both sides of the equation by 4 to eliminate the denominator:
4(x) = 3y - 2
- Distribute the 4 to both terms in the parentheses:
4x = 3y - 2
- Add 2 to both sides of the equation to isolate the term with y:
4x + 2 = 3y
- Divide both sides of the equation by 3 to solve for y:
(4x + 2) / 3 = y
So, the value of y in terms of x is given by (4x + 2) / 3.
2. x = (y^3) / (3y^2 + y/2)
Similarly, to find the value of y in terms of x, we need to isolate y on one side of the equation. Here's how you can do it:
- Multiply the entire equation by the denominator (3y^2 + y/2) to eliminate the fraction:
x(3y^2 + y/2) = y^3
- Distribute x to both terms in the parentheses:
3xy^2 + xy/2 = y^3
- Move all terms to one side of the equation:
3xy^2 + xy/2 - y^3 = 0
- Factor out y:
y(3xy + x/2 - y^2) = 0
Now, we have two possible solutions for y:
1. y = 0
2. 3xy + x/2 - y^2 = 0
If y = 0, that means the value of y in terms of x is simply y = 0.
For the second solution, 3xy + x/2 - y^2 = 0, we would need additional information or another equation to solve for y.
I hope this helps! Let me know if you have any further questions.