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.