To solve the system of equations:

we first write the second equation in standard form, then we have the equivalent system:

Now we notice that, in the first equation, all the coefficients are multiple of 2 then we can write the system as:

Now, to eliminate one of the variables we need the coefficients of the same variable to be equal in both equations; to achieve this let's multiply the first equation by 3:

Now we subtract the second equation from the first and then we have:

once we know the value of y we plug it in the first equation and solve for x:

Therefore, the solution for the system of equations is x=4, y=-3