Question

Linear algebra question,

Say I have this system of equations

x = a + 4
y = a - 4
z = a


Now some people say that geometrically this means that 2 planes meet on a line.

Well I don't understand that statement. Can you please help me see what that means ? Thanks for reading.

Answer 1

ok, now, if x =a+4 , y = a-4, you have y = x -8 , right?

Answer 2

and if y = a-4, z = a, then z = y +4 ok?

Answer 3

from where did y = x -8 come from ?

Answer 4

y= a-4--> a = y+4
x = a+4 --> a = x -4
that gives y+4 = x-4 --> y = x-8

Answer 5

ok?

Answer 6

ok

Answer 7

ok with this pic?

Answer 8

k

Answer 9

now, on xy plane , we have y = x-8 , that is this plane

Answer 10

k

Answer 11

on zy plane, we have z = y+4, that is this plane

Answer 12

k

Answer 13

those planes intersect at