maxima solving linear equations

Question

I have some equations and I'm trying to find the value of $m_3+m_7+m_{11}+m_{15}$. All the variables are $\ge 0$ as a constraint (how to enter that?)

I can solve by paper/pen and get $34$ so I know this can be solved. However, I'd like to able to solve the same problem type with maxima and I just can't get the syntax right. Neither of these work and I can't figure it out from the documentation/google. The first gives no output and the second an error. I'm new to maxima so this is probably obvious to a better user of maxima. How should I be entering this?

solve([m8 + m9 + m10 + m11 + m12 + m13 + m14 + m15 = 55,
     m0 + m1 + m2 + m3 + m4 + m5 + m6 + m7 = 45,
     m4 + m5 + m6 + m7 = 1,
     m12 + m13 + m14 + m15 = 22,
     m2 + m3 + m6 + m7 = 45,
     m10 + m11 + m14 + m15 = 30,
     m1 + m3 + m5 + m7 = 9,
     m9 + m11 + m13 + m15 = 28,
     m5 + m7 = 0,
     m13 + m15 = 12,
     m3 + m7 = 9,
     m7 + m15 = 10,
     m1 + m9 = 1],m3+m7+m11+m15);

solve([m8 + m9 + m10 + m11 + m12 + m13 + m14 + m15 = 55,
     m0 + m1 + m2 + m3 + m4 + m5 + m6 + m7 = 45,
     m4 + m5 + m6 + m7 = 1,
     m12 + m13 + m14 + m15 = 22,
     m2 + m3 + m6 + m7 = 45,
     m10 + m11 + m14 + m15 = 30,
     m1 + m3 + m5 + m7 = 9,
     m9 + m11 + m13 + m15 = 28,
     m5 + m7 = 0,
     m13 + m15 = 12,
     m3 + m7 = 9,
     m7 + m15 = 10,
     m1 + m9 = 1],[m3,m7,m11,m15]);