I am lost as to how to find the solution to this equation:
x - 2z =1
y + z = 3
Correct answer:
x = 1 + 2r
y = 3 - r
z = r
Where did this r come from?! Why is it being used?
r is called a parameter, you have 3 unknowns and 2 equations which if you recall from high school algebra, means you do not have enough info to find a solution
when we say z=r and y=3-r and x=1+2r what this really means is you have enough info to determine y=3-z and x=1+2z, but because we lack a 3rd equation you can let z be anything
So particular solutions are of the form (1+2r,3-r,r) where you pick some number for r and then plug it in