Solve the system of equations: 10x - 13y + 2 = 0, 26y = 20x + 5.

Step 1: Rewrite the first equation as 10x - 13y = -2.

Step 2: Rewrite the second equation as -20x + 26y = 5.

Step 3: Multiply the first equation by 2: 20x - 26y = -4.

Step 4: Add the modified first equation to the second equation: (20x - 26y) + (-20x + 26y) = -4 + 5, which simplifies to 0 = 1. This indicates that the system has no solution.