Graphical Methods of Solving Linear System of Equations

Graphical (approximate, limited to 2x2 system)
ex. 
2 x  - 1 y = 2  ==>  y =  2 x  - 2 (slope = 2, y-intercept = -2)
8 x + 2 y = 4  ==>  y = -4 x + 2 (slope = -4, y-intercept = 2)

Solution of
x » 0.65
y » -0.65
This method is inaccurate and tedious.

Inconsistent System (No Solution)
eg.
x - y = -1  ==> y = x + 1
x - y =  2  ==> y = x - 2

Lines have same slope, different y-intercepts

--> do not intersect

--> no solution to this system

Note: An attempt to solve this system algebraically will lead to mathematical non sense like 1 = -2 or 0 = 4,... Inconsistent system

eg.

2  x + 4 y = 2               ==> y = -1/2 x + 1/2
                          }∆
-4 x - 8 y = -4              ==> y = -1/2 x + 1/2

two lines represent the same equation
--> infinite number of solutions for system ∆

Note: An attempt to solve such a system algebraically will lead to something like 0 = 0; 2 = 2; 5 = 5,... Redundant system