The solution to the system of equations is (x, y) = (25/16, 205/144).
To solve the system of equations:
Start by rearranging the second equation, 9y = 5x + 5, to get y = (5/9)x + 5/9.
Substitute this value of y into the first equation, 3x - 7y = 5, to get 3x - 7((5/9)x + 5/9) = 5.
Simplify the equation to get (32/9)x - (35/9) = 5.
Add (35/9) to both sides of the equation to get (32/9)x = 5 + (35/9).
Simplify further to get (32/9)x = (50/9).
Divide both sides by (32/9) to solve for x, giving x = (50/9) / (32/9).
Perform the division to get x = 50/32 = 25/16.
Substitute this value of x into the equation y = (5/9)x + 5/9 to solve for y, giving y = (5/9)(25/16) + 5/9.
Perform the multiplication and addition to get y = 125/144 + 5/9.
Combine the two fractions to get y = (125 + 80)/144.
Simplify further to get y = 205/144.
Therefore, the solution to the system of equations is (x, y) = (25/16, 205/144).