Final answer:
The system of linear equations -6 + 5x = 6y and 4y + 14 = 5x are solved to obtain the solution as (x, y) = (6, 4), matching option (c).
Step-by-step explanation:
The problem presented involves solving a system of linear equations. The given system is:
- -6 + 5x = 6y (1)
- 4y + 14 = 5x (2)
To solve the system, you can express equation (2) with y on one side to get:
y = (5x - 14)/4 (3)
Replace y in equation (1) with the expression from equation (3) to solve for x:
-6 + 5x = 6((5x - 14)/4)
Multiply both sides by 4 to clear the denominator:
-24 + 20x = 30x - 84
Combine like terms:
-24 + 84 = 30x - 20x
60 = 10x
x = 6
Now, substitute x back into equation (3) to solve for y:
y = (5(6) - 14)/4
y = (30 - 14)/4
y = 16/4
y = 4
The solution to the system of equations is (x, y) = (6, 4), which corresponds to option (c).