Algebraic view of systems of equations

Which of the following equations are linear?

1. $2x-3y+4z=-10$

2. $2.123x_{1}+5.541x_{2}-9.101x_{3}=11.012$

3. $x^{2}+y^{2}+z^{2}=1$

4. $\frac{1}{\sqrt{2}}x+4^{3}y=\sin(\frac{\pi}{3})$

5. $x+yz=3$

Consider the system of equations

For each of the following tuples $(x,y,z,w)$ of real numbers, determine whether it is a solution of the first equation, second equation, and/or third equation. Which ones are solutions to the system of equations?

(a) $(2,0,-2,2)$  (b) $(2,2,-2,0)$  (c) $(1,1,-1,1)$  (d) $(3,0,-1,1)$  (e) $(2,-2,2,0)$