10. 13(m - 2) = -4(11 + m) + 1\n12. 2(12 - y) = 23 - (2y - 1)

Explanation:

Step1: Expand both sides of the equation

For (13(m - 2)=-4(11 + m)+1), using the distributive property (a(b + c)=ab+ac), we get (13m-26=-44 - 4m+1). Simplify the right - hand side: (13m-26=-43 - 4m). For (2(12 - y)=23-(2y - 1)), expand the left - hand side using the distributive property: (24-2y = 23-2y + 1). Simplify the right - hand side: (24-2y=24-2y).

Step2: Solve the first equation (13m-26=-43 - 4m)

Add (4m) to both sides: (13m + 4m-26=-43-4m + 4m), which gives (17m-26=-43). Add (26) to both sides: (17m-26 + 26=-43+26), so (17m=-17). Divide both sides by (17): (m=\frac{-17}{17}=-1). For the second equation (24-2y=24-2y), subtract (24) from both sides: (24-24-2y=24-24-2y), which gives (0 = 0). This means the equation is an identity and (y) can be any real number.

Answer:

For (13(m - 2)=-4(11 + m)+1), (m=-1). For (2(12 - y)=23-(2y - 1)), (y\in R) (where (R) represents the set of all real numbers).