6y = 12x + 36 15y = 45x + 60

The system has no solution
The system has exactly one solution
The system has infinitely many solutions

Equation 1: 6y = 12x + 36

Equation 2: 15y = 45x + 60

Solve equation 1 for y by dividing both sides by 6 to get: y = 2x + 6

Replace y in equation 2:

15(2x + 6) = 45x + 60

Simplify:

30x + 90 = 45x + 60

Subtract 45x from both sides:

-15x + 80 = 60

Subtract 90 from both sides

-15x = -30

Divide both sides by -15:

X = 2

Now replace x in the first equation and solve for y:

6y = 12(2) + 36

6y = 24 + 36

6y = 60

Divide both sides by 6

Y = 10

The solution is x = 2, y = 10

The answer is there is only one solution.

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step-by-step explanation: