You are given that y=x+1 so simply substituting this value of y into the first equation is the simplest way to start...3x=3y-3 becomes:
3x=3(x+1)-3 perform indicated multiplication on right side
3x=3x+3-3 combine like terms on right side
3x=3x this is true for any real value of x so there are infinitely many solutions.
Which might be easier to see if you divide the first equation by 3...
3x=3y-3 divide entire equation by 3
x=y-1 add 1 to both sides
x+1=y or
y=x+1 which is equal to the second original equation.
So essentially the two equations are the same line, that is why there are infinitely many solutions as each point on one line is equal to the same point on the "other" line.