The system of equations

2x - y + 1 = 0 ...(1)

x + 2y - 6 = 0 ...(2)

has to be solved.

(1) - 2*(2)

=> 2x - 2x - y - 4y + 1 + 12 = 0

=> -5y = -13

=> y = 13/5

x = 6 - 2y = 6 - 26/5 = 4/5

To check the solution, substitute x and y in the equations and check the result.

2x - y + 1 = 2*(4/5) - (13/5) + 1 = 0

x + 2y - 6 = 4/5 + 26/5 - 6 = 0

**The solution of the given system of equations is x = 4/5 and y = 13/5**