Solve a system equation

by naoufelabs
Tags: equation, solve
 P: 17 Hi everybody, Please I want to Solve the system: 3x-2y=19 y3-2x=19 x,y real number! Thank you !
 Mentor P: 12,045 I think clever guessing (and showing that there are not other solutions) is the quickest method. You can solve one of those equations for a single variable and put this into the other equation, but I don't think you cannot simply find solutions like that.
 Sci Advisor HW Helper P: 11,948 It looks like 3,3 is the only solution.
 Mentor P: 12,045 Solve a system equation There is another solution near y=20.8216, x=13.1370.
 P: 17 Please I want the steps to find it, because I'm stumbled in the last steps as follow: x*Ln(3)-y*Ln(2)=Ln(19) 3*Ln(y)-x*Ln(2)=Ln(19) x*Ln(3)-y*Ln(2) - 3*Ln(y)-x*Ln(2) = 0 x*Ln(3)+x*Ln(2) = y*Ln(2)+3*Ln(y) {each one equals Ln(19)} x*Ln(3)+x*Ln(2) = y*Ln(2)+3*Ln(y) = Ln(19) x*Ln(6) = y*Ln(2)+3*Ln(y) = Ln(19) x = ln(19)/ln(6) ..... Here I'm stumbled. Thank you for your response.
 Mentor P: 12,045 There is no useful way to simplify ln(19)/ln(6). It is just some number - and it is wrong. The first step does not work. ln(a-b) is not the same as ln(a) - ln(b). The third step looks wrong, too (where you say "{each one equals Ln(19)}").
Mentor
P: 21,397
 Quote by naoufelabs 3x-2y=19 y3-2x=19 x,y real number!
The first equation below is wrong, so everything below it is also invalid.

You apparently took the natural log of both sides, like so:
ln(3x - 2y) = ln(19)

Then you "distributed" the ln operation like this:
ln(3x) - ln(2y) = ln(19)
This is the step that is incorrect. There is no property of logs in which ln(A + B) = ln(A) + ln(B).

 Quote by naoufelabs Please I want the steps to find it, because I'm stumbled in the last steps as follow: x*Ln(3)-y*Ln(2)=Ln(19) 3*Ln(y)-x*Ln(2)=Ln(19) x*Ln(3)-y*Ln(2) - 3*Ln(y)-x*Ln(2) = 0 x*Ln(3)+x*Ln(2) = y*Ln(2)+3*Ln(y) {each one equals Ln(19)} x*Ln(3)+x*Ln(2) = y*Ln(2)+3*Ln(y) = Ln(19) x*Ln(6) = y*Ln(2)+3*Ln(y) = Ln(19) x = ln(19)/ln(6) ..... Here I'm stumbled. Thank you for your response.
 P: 17 Thank you all.

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