\(Solve[{x + 2  y - 3  z\  + 
            4  u == \(-1\), 
	\ x + 2  a\ y + 7  z + 
            10  u == \(-5\), 
	\((a - 1)\) 
              y + \((b + 3)\) z + \((a + 2)\) u == b - 4, \ 
        a ≠ 1, \ z\  == \ α}, \ {x, y, z, 
        u}]\)

{FullSimplify[-((25 - 14 a + (a^2) - 10 b + 4 a b - 
                  13 α + 4 a α - 3 (a^2) α + 
                  10 b α - 
                  4 a b α)/(((-1 + a))^2))] === 
        FullSimplify[
          3  α - 
            1 + ((4 + 10  α - 4 (b - 2) (1 - α))/((a - 1))) + ((6 (b - 2) (1 - α))/(((a - 1))^2))]}

{FullSimplify[-((-8 + 2 a + 3 b + α + 5 a α - 
                  3 b α)/(((-1 + a))^2))] === 
        FullSimplify[((2 + 5  α)/((1 - a))) - ((3 (b - 2) (1 - α))/(((a - 1))^2))]}

{FullSimplify[-((2 - b - 2 α + b α)/(-1 + 
                  a))] === 
        FullSimplify[(((b - 2) (1 - α))/(a - 1))]}

\(Solve[{x + 2  y - 3  z\  + 
            4  u == \(-1\), 
	\ x + 2  a\ y + 7  z + 
            10  u == \(-5\), 
	\((a - 1)\) 
              y + \((b + 3)\) z + \((a + 2)\) u == b - 4, \ a == 1, 
        b ≠ 2, \ y\  == \ α}, \ {x, y, z, 
        u}]\)

{FullSimplify[-(2/3) (-17 + 3 α)] === 
        FullSimplify[(34/3) - 2  α]}

\(Solve[{x + 2  y - 3  z\  + 
            4  u == \(-1\), 
	\ x + 2  a\ y + 7  z + 
            10  u == \(-5\), 
	\((a - 1)\) 
              y + \((b + 3)\) z + \((a + 2)\) u == b - 4, \ 
        a == 1, b == 2, \ y\  == \ α, \ 
        u == β}, \ {x, y, z, u}]\)

{FullSimplify[(1/5) (-11 - 10 α - 29 β)] === 
        FullSimplify[-2 α - ((29  β + 11)/5)]}

{FullSimplify[(1/5) (-2 - 3 β)] === 
        FullSimplify[-((3  β + 2)/5)]}