Systems Using Substitution
Key Questions

Well, I would say that it is easier when you have few equations and variables. If you have 2 equations and 2 variables it is ok; when you get to 3 equations and 3 variables it becomes more complicated, it is still possible, but you have more work to do. The number of substitutions increases together with the possibility to make mistakes.
More than 3 equations and 3 variables and it gets almost impossible and other methods would be better. 
For an answer to have an infinite solution, the two equations when you solve will equal
#0=0# .Here is a problem that has an infinite number of solutions.
#3x+2y= 12#
#6x4y=24# If you solve this your answer would be
#0=0# this means the problem has an infinite number of solutions.For an answer to have no solution both answers would not equal each other.
Here is a problem that has no solution.
#4x8y=5#
#3x+6y=11# Again, if you solve this your answer would be
#0=59# , this is obviously not true, 0 does not equal 59 so this problem would have no solution. 
Answer:
Please see below.
Explanation:
I assume you are interested in linear equations. In general you need
#n# equations if you have#n# variables.Let us have
#3# equations and#3# variables#x,y# and#z# . Now pick up an equation with#x# and segregate it say#x# in terms of#y,z# . When we put this value of#x# in two other equations we get two equations in#y# and#z# .We can now find
#y# in terms of#z# say using second equation and when we put in third equation we get value of#z# .Once
#z# is known, it is easy to find#y# and then#x# .