How many solutions does the system have? x = -6y + 3
5x + 30y = 15
one solution
two solutions
infinitely many solutions
no solution

infinitely many solutions

Step-by-step explanation:

we have: x+6y= 3

5x+30y=15

where a1/a2 = b1/b2 = c1/c2 (1/5 = 6/30 = 3/15)

Thus, the system has infinitely many solutions.

another approach:

convert to slope-intercept form

y= -1/6x + 1/2

y= -1/6x + 1/2

thus, the system has infinitely many solutions.

(explain: if two lines have a same slope (-1/6), they can be either parallel or coincided. But in this case, they also have a same y-intercept so they must be the latter case)