# Math Help - 3 Simulataneuous Eqn

1. ## 3 Simulataneuous Eqn

27x+37y+47z=212
37x+47y+27z=212
47x+27y+37z=242

2. You can solve this using substitution, Cramer's rule, lineair combinations, putting it in a matrix and row reducing... What do you know and what have you tried, or where are you stuck?

3. You do use a number of methods to solve this. You could use matrices, substitution, or add/subtract the equations together to cancel out variables. Are you familiar with these methods?

I think substitution would be the easiest. For one equation, solve for x in terms of the other two variables. So now you can have an equation of two variables. Then solve for one of the other variables and you should have an equation down to only one.

4. You can solve for $z$ easily. Add all your equations to get $111x+111y+111z=666$ thus, $x+y+z=6$. Now the first equation is equal to the second one thus
$27x+37y+47z=37x+47y+27z$ which becomes
$x+y-2z=0$ Now subtract these two equation and you get $z=2$ once you know $z$ you can easily solve for $x,y$.
Q.E.D.