simultaneous equation

Question

3x+2y=14 and 2xy+5=21                                      .       please solve algebraically

Answer 1

Hello Joseph,

 

3x + 2y = 14

 

2xy + 5 =21

 

Let's make y the subject of formula in both equations 

 

3x + 2y  = 14 becomes  2y = 14 - 3x

 

And 2xy + 5 = 21 becomes 2xy = 21 -5 then becomes y = (21 -5)/2x = 16/2x = 8/x

 

y = 8/x

 

Then plug in 8/x for y in the first equation

 

2y = 14 - 3x  becomes  2 (8/x) = 14 - 3x

 

we now have 16 = 14 x - 3x^2

 

0 = 14x - 3x^2 - 16

 

you can multiply each term by negative 1 to change the sign if you want

 

if you did, then you would have

 

3x^2 -14x +16 = 0

 

Factories this to get (3x - 8) (x -2) = 0 

 

3x -8 = 0, x - 2 = 0

 

so x = 8/3 or x = 2 and we will choose x = 2

 

Plug in  x = 2 for y = 8/x to get y = 4

 

now you have it x = 2, y = 4