Solve the system of equations: [x-7y=3, 14y-2x=-6.

Multiply the first equation by 2:

2(x - 7y) = 2(3) => 2x - 14y = 6

Add this new equation to the second equation:

(2x - 14y) + (14y - 2x) = 6 + (-6)

0 = 0

This indicates that the two equations are dependent, meaning there are infinitely many solutions. Any pair (x, y) that satisfies one equation will satisfy the other. For example, if x = 3, then -7y = 0, so y = 0. Thus, (3, 0) is a solution. If y = 0, then x = 3. If x = 0, then -7y = 3, so y = -3/7. Thus, (0, -3/7) is a solution.