y = 3x, 2y^2 - xy = 15

Question

it's a simultaneous equation problem need ur help badly ;()..

Answer 1

Hi Rodela;

y=3x

2y²-xy=15

Let's substitute y with 3x...

[2(3x)²]-[(x)(3x)]=15

[2(9x²)]-3x²=15

18x²-3x²=15

15x²=15

Let's divide both sides by 15...

(15x²)/15=15/15

x²=1

x=+1 and -1

y=3x

y=(3)(1)=3

y=(3)(-1)=-3

y=+3 and -3

 

 

Answer 2

y = 3x => x = y/3

 

2y^2 - xy = 15

 

2y^2 - (y/3)y = 15

 

Multiply both sides by 3:

 

6y^2 - (y)y = 45

 

5y^2 = 45

 

y^2 = 9

 

y = ±3

 

x = y/3

 

Solutions are (1,3) and (-1,-3)

Answer 3

 Y = 3X

 

  2Y^2 - XY = 15

 

In Simultaneous systems other than linear systems, only available procedure  is the substitution method.

 

     Substitute 3X for Y in 2nd equation

 

     2( ( 3X) ^2) - X ( 3X) = 15

 

    18 X^2 - 3X^2 = 15

 

      15 X^2 = 15          X^2 = 1     X = ±1     Y =±3