how do i verify a question when i am solving for Y..
yet i need to subsatoute X first to find Y. such as in this probelm to find Y
((xy)/(x+4)-(2y/x)=3 solve for Y
i end up with........lets say that X=4
Y= (3x^2+12x)/(x^2-2x+8)
Y=6
now how am i supposed to verify am i supposed to be getting 3 as my answer and if so how does that work when i have to subsatue X to find Y
To verify the solution for Y, you need to substitute the calculated value of Y back into the original equation and see if it satisfies the equation.
Let's start by solving the equation for Y:
((xy)/(x+4)) - (2y/x) = 3
To eliminate the denominators, let's multiply both sides of the equation by (x+4) and x:
x(x+4)((xy)/(x+4)) - x(x+4)((2y/x)) = 3(x+4)(x)
This simplifies to:
xy - 2(x+4)y = 3x(x+4)
Now, let's distribute and rearrange the terms:
xy - 2xy - 8y = 3x^2 + 12x
Combine like terms:
-xy - 8y = 3x^2 + 12x
Next, let's isolate the variables on one side of the equation:
-xy - 8y - 3x^2 - 12x = 0
Now, factor out the common term of y:
y(-x - 8) - 3x(x + 4) = 0
Finally, let's solve for y:
y = (3x(x + 4)) / (-x - 8)
Now that we have the equation for y, let's substitute x = 4 into the equation to find the corresponding value of y:
y = (3(4)(4 + 4)) / (-4 - 8)
y = (3(4)(8)) / (-12)
y = 96 / -12
y = -8
Now, to verify if y = -8 is the correct solution, substitute x = 4 and y = -8 back into the original equation:
((xy)/(x+4)) - (2y/x) = 3
((4(-8))/(4+4)) - (2(-8)/4) = 3
(-32/8) - (-16/4) = 3
-4 + 4 = 3
0 = 3
Since 0 is not equal to 3, our assumed solution y = -8 is incorrect.
To find the correct solution, you may need to recheck your calculations and steps taken to solve for y. Double-check for errors or potential mistakes made during the process.