Which of the following ordered pairs is a solution to the system: 6x - 2y = 2 9x - 3y = 1

(4,2)

To find the solution to the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. One way to solve this is by using the method of substitution.

Let's solve for one variable in terms of the other and then substitute it into the other equation.

From equation 6x - 2y = 2, we can solve for x:

6x = 2y + 2

Divide both sides by 6:

x = (2y + 2) / 6

Now, substitute this value of x into the second equation 9x - 3y = 1:

9((2y + 2) / 6) - 3y = 1

Multiplying through by 6 to clear the fraction, we get:

9(2y + 2) - 18y = 6

Distribute 9:

18y + 18 - 18y = 6

Combine like terms:

18 = 6

This is not true, which means the system of equations has no solution.

Therefore, none of the ordered pairs is a solution to the system.