# Math Help - equations reduced

1. ## equations reduced

Finding the equations reduced with x independent variable of straight intersection of plans

$n1: 3x-2y-z-1=0$

$n2: x+2y-z-7=0$

$y=\frac{1}{2}x+\frac{3}{2}$
$z=2x-4$

2. Originally Posted by Apprentice123
Finding the equations reduced with x independent variable of straight intersection of plans

$n1: 3x-2y-z-1=0$

$n2: x+2y-z-7=0$

$y=\frac{1}{2}x+\frac{3}{2}$
$z=2x-4$
Hey you should be able to do this.

The common line lies on both n1 and n2. Thus both equations must be satisfied for points on the intersection . So first eliminate z by subtracting n2 from n1,

$n1-n2: 3x-2y-z-1- (x+2y-z-7) = 2x - 4y + 6 =0 \Rightarrow y = \frac{2x}{4} + \frac64 = \Rightarrow y = \frac{x}2 + \frac32$

Now do the other one please... Its easy, just eliminate y!

3. Thank you