Answer: We can solve this system of equations using elimination as follows:
9x + 15y = 6
5y = -3x + 2
To eliminate y, we can multiply the second equation by -3 and add it to the first equation:
9x + 15y = 6
-15y = 9x - 6
Simplifying the second equation, we get:
-5y = 3x - 2
Now we have two equations in terms of x and y:
9x + 15y = 6
-5y = 3x - 2
If we multiply the second equation by -3 and add it to the first equation, we get:
9x + 15y = 6
15y - 9x = 6
Simplifying, we get:
6y = 2
Dividing by 6, we get:
y = 1/3
Substituting y into the second equation, we get:
5(1/3) = -3x + 2
Simplifying, we get:
-3x = -13/3
Dividing by -3, we get:
x = 13/9
Therefore, the solution to the system of equations is (x, y) = (13/9, 1/3).
Mandy's statement that the system has no solutions is false. The system has a unique solution.
Explanation: