Find y x </mfrac> from 3 x + 3 y = y t = x t

Finley Mckinney

Finley Mckinney

Answered question

2022-06-22

Find y x from 3 x + 3 y = y t = x t + 2.5 x I need to find the ratio of
y x
If given that
3 x + 3 y = y t = x t + 2.5 x
So what I tried is:
t = 3 x + 3 y y
And then put it in the equation
x ( 3 x + 3 y ) y + 2.5 x = ( 3 x + 3 y ) y y
x ( 3 x + 3 y ) y + 2.5 x = 3 x + 3 y
3 x 2 y + 3 y x y + 2.5 x = 3 x + 3 y
3 x 2 y + 3 x + 2.5 x = 3 x + 3 y
3 x 2 y + 2.5 x = 3 y
Here I got stuck. I didn't know how to find the ratio. Can someone help me?

Answer & Explanation

iceniessyoy

iceniessyoy

Beginner2022-06-23Added 27 answers

Assuming your calculations so far are correct (I didn't check), you are almost there. Divide both sides by y, you will get
3 x 2 y 2 + 2.5 x y = 3 ,
a quadratic equation for x y .
Hector Petersen

Hector Petersen

Beginner2022-06-24Added 6 answers

It is given that
3 x + 3 y = y t = x t + 2.5 x
This implies
t = 3 x + 3 y y = 0.5 x + 3 y x
3 x 2 + 2.5 x y 3 y 2 = 0
3 ( y x ) 2 + 2.5 y x + 3 = 0
y x = 2.5 ± 42.25 6
Hence
y x = 3 2 , 2 3

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