The correct option is C. (2, 1).
Given equations:
y = 6x - 11
2x + 3y = 7
We'll start by solving equation 1) for y:
y = 6x - 11
Now, substitute this value of y into equation 2):
2x + 3(6x - 11) = 7
Simplify the equation:
2x + 18x - 33 = 7
20x - 33 = 7
Add 33 to both sides:
20x = 40
Divide both sides by 20:
x = 2
Now, substitute the value of x back into equation 1) to find y:
y = 6(2) - 11
y = 12 - 11
y = 1
Therefore, the solution to the system of equations is (x, y) = (2, 1).