# Simultaneous Equation

• Mar 23rd 2008, 10:55 PM
scarybear12
Simultaneous Equation
y = 2x - 6
x^2 - xy + 2y^2 = 16
• Mar 23rd 2008, 11:08 PM
o_O
You are given y in terms of x, so directly substitute:

$\displaystyle x^{2} - x\bold{y} + 2\bold{y}^{2} = 16$
$\displaystyle x^{2} - x\left(\bold{2x-6}\right) + 2\left(\bold{2x-6}\right)^{2} = 16$

Continue and solve for x.
• Mar 24th 2008, 12:48 AM
a.a
y = 2x - 6
x^2 - xy + 2y^2 = 16

=> x^2 - x (2x-6) + 2(2x-6)^2 = 16
x^2 - 2 x^2 + 6x + 2( 4x^2 -12x + 36) = 16
-x^2 + 6x + 8x^2 -24x + 72 -16 = 0
7x^2 - 18x + 56=0

use the quadraic eqn. to solve for x, then when u get the two x values, plug it into y = 2x - 6 and u the two y values
• Mar 24th 2008, 06:39 AM
o_O
Quote:

Originally Posted by a.a
y = 2x - 6
x^2 - xy + 2y^2 = 16

=> x^2 - x (2x-6) + 2(2x-6)^2 = 16
x^2 - 2 x^2 + 6x + 2( 4x^2 -12x + 36) = 16
-x^2 + 6x + 8x^2 -24x + 72 -16 = 0
7x^2 - 18x + 56=0

use the quadraic eqn. to solve for x, then when u get the two x values, plug it into y = 2x - 6 and u the two y values

Should be: $\displaystyle x^{2} - 2x^{2} + 6x + 2(4x^{2} - \bold{24x} + 36) = 16$