Given the system of linear equations:
\(\left\{ x + 6y = 6
\right.\) y = 1/3x - 2

part a: graph the system of linear equations.
part b: use the graph created in part a to determine the solution to the system.
part c: algebraically verify the solution from a part b

Step-by-step explanation:

hello :

Part A :  x+6y =6 means : 6y = - x+6

so : y = (-1/6)x+1  an equation for the line (D)

     y = (1/3)x -2 is the line (D')

PartB : solution of the system  : y = (-1/6)x+1 ....(1)    color  red

                                        y =  (1/3)x -2 ....(2)  color  bleu

is the intersection point : (6 ; 0)

PartC : Algebraically  by (1) and (2) : (-1/6)x+1 =  (1/3)x -2

(-1/6)x  - (1/3)x = -2-1

(-x-2x)/6= -3

-3x = -18

so : x = 6  put this value in (1) or (2) : y = (-1/6)(6)+1 =0 the solution is : (6 ;0)