Linear system equations - plan intersection?

how to find out where is the plane intersection of:

x+y+z=3
x+2y+2z=4

I started doing

clc
clear
format compact
syms x y z
ekv1=x+y+z==3
ekv2=x+2*y+2*z==4

Answer 1

[Roger Stafford]

Each of these equations defines a plane. Their intersection will in general be a single straight line. You can define a straight line by locating any two points on the line. For example, let y = 0. Then solving the two resulting equations for x and z gives (2,0,1) for the (x,y,z) values. Then let y = 1. Solving for x and z this time gives (2,1,0). Thus (2,0,1) and (2,1,0) are two points on the intersection line.