Can I and how would I solve 5x 6y-23 and 2x-5y13 (system of equations) without using a calculator?

Without any equality signs and not knowing some of the minus or plus values of the given terms we can't considered it to be a system of simultaneous equations but if you meant: 5x+6y = -23 and 2x-5y = 13 then by multiplication, elimination and substitution the values of x and y work out as x = -1 and y = -3