We know that when a consistent system has infinite solutions, then the graphs of the equations are exactly the same. In other words, these equations are called dependent equations.
All points of dependent equations share the same slope and same y-intercept.
For example,
6x-2y = 18
9x-3y=27
represent the dependent equations.
Writing both equations in slope-intercept form
y=mx+c
where m is the slope and c is the y-intercept
Now
6x-2y=18
2y = 6x-18
Divide both sides by 2
y = 3x - 9
Thus, the slope = 3 and y-intercept = b = -9
now
9x-3y=27
3y = 9x-27
Divide both sides by 3
y = 3x - 9
Thus, the slope = 3 and y-intercept = b = -9
Therefore, both equations have the same slope and y-intercept. Their graphs are the same. Hence, they are called dependent equations.
