As I explained in my comment to @Vasishta Bhargava, this is a problem with 3 equations, but only 2 unknowns. It is known as an over-determined problem. As such, it likely never has an exact solution, so solve cannot solve it.
Typically, one might use a tool like a linear regression, to find y2 and z2 that will minimize the errors in the three equations at once. I'll be lazy here and just use fminsearch.
new = @(yz) [(29*yz(1))/5 - (7*yz(2))/10, 7*yz(2), -7*yz(1)];
dif = [-0.1337 -9.7234 1.3349];
obj = @(yz) norm(new(yz) - dif);
yz = fminsearch(obj,[1 1])
How well did it work?
-0.133719852295332 -9.72331610177938 1.33488969608843
-0.1337 -9.7234 1.3349
quite well in fact.
I could also have use a direct linear regression.
[A,B] = equationsToMatrix(eqn);
So the same answer, but this time it is more precise, since fminsearch uses a tolerance.