Help With Simultaneous Equations

**M0000** · July 25th 2012, 10:53 PM

So i'm having trouble with simultaneous equations, the equations are:

y^2 + x^2 = 150^2
3y + 2x = 180

Looks quite simple but i'm not sure where to get started mainly because of the '150^2'.
Please help.

**BAdhi** · July 26th 2012, 01:32 AM

you can isolate $y$ (or x) from the second equation, so that

$y=60-\frac{2x}{3}$

then substitute it to the first equation,

$\begin{align*}\left(60-\frac{2x}{3}\right)^2+x^2 &=150^2\\60^2-\frac{2\times 60\times 2x}{3}+\frac{4x^2}{9}+x^2&=150^2\\\frac{4x^2}{9}+x ^2-80x+(60-150)(60+150)&=0\\13x^2-720x+9\times (-90)\times 210&=0\\13x^2-720x-170100&=0 \end{align*}$

this is a quadric equation, hope you can solve it

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