Final answer:
To solve the system of equations 2x - 6y = 10 and -3x + 9y = -15, we can use the method of elimination. The system has infinitely many solutions, which can be expressed in the form (x, y), where x is any real number and y is determined by the equation -3x + 9y = -15.
Step-by-step explanation:
To solve the system of equations 2x - 6y = 10 and -3x + 9y = -15, we can use the method of elimination. We will eliminate x by multiplying the first equation by -3 and the second equation by 2, and then adding the two equations together.
Multiplying the first equation by -3, we get -6x + 18y = -30. Multiplying the second equation by 2, we get -6x + 18y = -30. Subtracting the second equation from the first equation, we get 0 = 0.
Since 0 = 0, this means that the two equations are dependent, and the system has infinitely many solutions. The solution set can be expressed in the form (x, y), where x is any real number and y is determined by the equation -3x + 9y = -15.