Step 1: Solve the first equation for x in terms of y.
9x = 39 - 2y
x = (39 - 2y)/9
Step 2: Substitute the value of x from the first equation into the second equation.
6((39 - 2y)/9) + 13y = 9
Step 3: Simplify and solve for y.
(234 - 12y)/9 + 13y = 9
(234 - 12y + 117y)/9 = 9
105y + 234 = 81
Step 4: Solve for y.
105y = 81 - 234
105y = -153
y = -153/105
y = -1.4571
Step 5: Substitute the value of y back into the first equation to solve for x.
9x + 2(-1.4571) = 39
9x - 2.9142 = 39
9x = 39 + 2.9142
9x = 41.9142
x = 41.9142/9
x = 4.6571
Therefore, the solution to the system of equations is:
x = 4.6571
y = -1.4571