# Math Help - simultaneous equation

1. ## simultaneous equation

Solve the simultaneous equation:

$x-2y+3=0$

$x^2+xy-27=0$

2. Originally Posted by mastermin346
Solve the simultaneous equation:

$x-2y+3=0$

$x^2+xy-27=0$
Dear mastermin346,

Subject "y" in the first equation and substitute it in the second equation. Then you would have a quadratic equation.

Hope this helps.

3. Originally Posted by mastermin346
Solve the simultaneous equation:

$x-2y+3=0$

$x^2+xy-27=0$
From the first equation, we can see that $x = 2y - 3$.

Substituting into the second equation:

$(2y - 3)^2 + (2y - 3)y - 27 = 0$

$4y^2 - 12y + 9 + 2y^2 - 3y - 27 = 0$

$6y^2 - 15y - 18 = 0$

$2y^2 - 5y - 6 = 0$

$y^2 - \frac{5}{2}y - 3 = 0$

$y^2 - \frac{5}{2}y + \left(-\frac{5}{4}\right)^2 - \left(-\frac{5}{4}\right)^2 - 3 = 0$

$\left(y - \frac{5}{4}\right)^2 - \frac{25}{16} - \frac{48}{16} = 0$

$\left(y - \frac{5}{4}\right)^2 - \frac{73}{16} = 0$

$\left(y - \frac{5}{4}\right)^2 = \frac{73}{16}$

$y - \frac{5}{4} = \pm \frac{\sqrt{73}}{4}$

$y = \frac{5 \pm \sqrt{73}}{4}$.

So substitute $y = \frac{5 - \sqrt{73}}{4}$ and $y = \frac{5 + \sqrt{73}}{4}$

into $x = 2y - 3$

to find the two values of $x$.