Question

graph and determine the solution of the system
y = 6x - 3
\\(\frac{1}{3}y = 2x - 1\\)

use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Simplify the second equation

Multiply both sides by 3:
$$\frac{1}{3}y \times 3 = (2x - 1) \times 3$$
$$y = 6x - 3$$

Step2: Compare the two equations

The first equation is $y = 6x - 3$, and the simplified second equation is also $y = 6x - 3$. This means the two lines are identical (coinciding).

Step3: Determine the solution set

Coinciding lines have infinitely many points in common, so every point on the line is a solution.

Answer:

The system has infinitely many solutions, represented by all points on the line $y = 6x - 3$.