There is a little ambiguity, but I'll assume that the last term is1/(3Y), not (1/3)Y (repetit assumption). In that case, multiply all terms by Y and you will get a quadratic equation in Y, with X as part of the coefficient of the linear term. Solve the quadratic for Y and you will have your answer (actually two answers).X=(Y-2)/3 - 1/3Y
You forgot a 3 there. It's correct on the next line though.yx=(y^2 - 2y)/3 - 1/3
yx=(y^2 - 2y - 1)
Are you sure? Check what happens if you work out the brackets in the second line. I think it's a minus sign off.y^2 - 2y - 1 - 3yx=0
y^2 - y(2-3x) - 1 = 0
To find Y in terms of X, you will need to rearrange the equation so that Y is isolated on one side of the equals sign. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division on both sides of the equation. By doing this, you will be able to express Y as a function of X.
Finding Y in terms of X is important because it allows us to understand the relationship between two variables. It also helps us to solve equations and make predictions or calculations based on the given information.
Sure, let's say we have the equation 4x + 2 = 3y and we want to find Y in terms of X. We can start by subtracting 2 from both sides to get 4x = 3y - 2. Then, we can divide both sides by 3 to get (4/3)x = y - (2/3). Finally, we can add (2/3) to both sides to get y = (4/3)x + (2/3). This is Y expressed in terms of X.
Some common mistakes to avoid when finding Y in terms of X include forgetting to perform the same operation on both sides of the equation, using the wrong order of operations, and making calculation errors. It is important to double check your work and simplify your final answer.
The equation Y = mx + b is known as the slope-intercept form, where m represents the slope and b represents the y-intercept. To find Y in terms of X using this equation, you can simply rearrange it to get mx = Y - b, and then divide both sides by m to get x = (Y - b)/m. This is Y expressed in terms of X.