To determine if the ordered pair (3, 1) is a solution to the system of equations:
x + 5y = 8
4x - 5y = 7
We substitute x = 3 and y = 1 into both equations and check if the equations hold true.
x + 5y = 8
3 + 5(1) = 8
3 + 5 = 8
8 = 8
This equation is true when x = 3 and y = 1.
4x - 5y = 7
4(3) - 5(1) = 7
12 - 5 = 7
7 = 7
This equation is also true when x = 3 and y = 1.
Since both equations hold true for the values x = 3 and y = 1, we can conclude that the ordered pair (3, 1) is a solution to the system of equations.