To solve this system of equations, we can use either substitution or elimination method.

Substitution method:

1. Solve one of the equations for one variable in terms of the other. For example, from the first equation, we can solve for x:

x = 7 - 5y

2. Substitute the expression we found for x into the other equation and solve for y:

3(7 - 5y) - 2y = 4

21 - 15y - 2y = 4

-17y = -17

y = 1

3. Substitute the value we found for y back into one of the original equations and solve for x:

x + 5(1) = 7

x = 2

Therefore, the solution to the system of equations is (2, 1).

Elimination method:

1. Multiply the first equation by 2 and the second equation by 5 to eliminate the y variable:

2x + 10y = 14

15x - 10y = 20

2. Add the two equations together to eliminate y:

17x = 34

x = 2

3. Substitute the value we found for x back into one of the original equations and solve for y:

2 + 5y = 7

5y = 5

y = 1

Therefore, the solution to the system of equations is (2, 1), which is the same as the solution we found using substitution method.