You are Here: Home

# Geometric representations of simultaneous equations watch

1. I've found myself with the simultaneous equations

3x + 2y - z = 10
5x - y - 4z = 17
x + 5y + 2z = b

I think the equations are inconsistent unless b = 3.

Given that the equations represent three planes having a common line of intersection, find the line in the (x - p)/l = (y - q)/m = (z - r)/n form.

I think they're referring to the case b = 3 here, since any other case the equations have no solutions and the planes don't intersect. I'm stuck on how to find the line of the solutions in the case where b = 3, I've never been taught this. (Or roots of unity for that matter. Neglegant teacher?)
2. well, stick b=3 in. then try and solve the equations normally, but you will be left with a relation between x,y, and z, which will be the equation of the line that they are asking you to look for.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 26, 2004
Today on TSR

### University open days

• University of East Anglia (UEA)
Could you inspire the next generation? Find out more about becoming a Secondary teacher with UEA… Postgraduate
Thu, 18 Oct '18
• University of Warwick
Sat, 20 Oct '18
• University of Sheffield