In[1]:= eq1 = 
  FullSimplify[(\[Lambda] \[Alpha] + \[Lambda] \[Mu] y) (p - \[Theta] \
x^2 - (1 - \[Theta]) y^2 - b - d) + (a - 
        k p + \[Lambda] (\[Alpha] x + (1 - \[Alpha]) y + \[Lambda] \
\[Mu] y)) (-2 \[Theta] x) == 0];
eq2 = FullSimplify[(\[Lambda] (1 - \[Alpha]) + \[Lambda] \[Mu] x) (p \
- \[Theta] x^2 - (1 - \[Theta]) y^2 - b - d) + (a - 
        k p + \[Lambda] (\[Alpha] x + (1 - \[Alpha]) y + \[Lambda] \
\[Mu] y)) (-2 (1 - \[Theta]) y) == 0];

In[3]:= AbsoluteTiming[Solve[Join[eq1, eq2], {x, y}];]

Out[3]= {0.627934, Null}

Are you running out of memory? My PC has 16 GBytes of RAM.

Mr. Frank Kampas you made ??a mistake.

We want to solve these equations:

eq1 = FullSimplify[1/2 ? y^(1/2) x^(-(1/2))(p - 1/2 x^2 - 1/2 y^2) + (a - k p + ? (x y)^(1/2)) (-x) == 0]
eq2 = FullSimplify[1/2 ? x^(1/2) y^(-(1/2))(p - 1/2 x^2 - 1/2 y^2) + (a - k p + ? (x y)^(1/2)) (-y) == 0]

not those:

eq1 = FullSimplify[(? ? + ? ? y) (p - ? x^2 - (1 - ?) y^2 - b - d) + (a - k p + ? (? x + (1 - ?) y + ? ? y)) (-2 ? x) == 0]
eq2 = FullSimplify[(? (1 - ?) + ? ? x) (p - ? x^2 - (1 - ?) y^2 - b - d) + (a - k p + ? (? x + (1 - ?) y + ? ? y)) (-2 (1 - ?) y) == 0]

My Laptop has 4 GBytes of RAM.With these 2 equations Kernel level of consumption of RAM is only 55MB and did not increase for the next hours calculating.

See file attachments:

Attachments:

Yes, you are right, transferring Windows version is not helpful. Let me try Maples. Thanks a lot.

Thanks for your help. I tried this method, but still no result, could you guide me your code? Thanks a lot.

Really appreciate your help. My MMA version is 10.2 too, but it is Mac version, not Windows version. I reduced the symbolic coefficients as much as possible, and still not work, should I transfer Windows version also?

Attachments:

Your system is of high degree with symbolic coefficients. A full symbolic solution may be too complicated. If you lower your expectations, you get quick explicit solutions for specific numeric values of the parameters, for example

With[{\[Lambda] = 1, \[Alpha] = -1, \[Mu] = 1, p = 1, \[Theta] = 1, 
  b = 1, d = 1, a = 1, k = 1},
 Solve[{(\[Lambda] \[Alpha] + \[Lambda] \[Mu] y) (p - \[Theta] x^2 - \
(1 - \[Theta]) y^2 - b - d) + (a - 
        k p + \[Lambda] (\[Alpha] x + (1 - \[Alpha]) y + \[Lambda] \
\[Mu] y)) (-2 \[Theta] x) == 
    0, (\[Lambda] (1 - \[Alpha]) + \[Lambda] \[Mu] x) (p - \[Theta] \
x^2 - (1 - \[Theta]) y^2 - b - d) + (a - 
        k p + \[Lambda] (\[Alpha] x + (1 - \[Alpha]) y + \[Lambda] \
\[Mu] y)) (-2 (1 - \[Theta]) y) == 0}, {x, y}]]

You can go interactive too:

Manipulate[
 ContourPlot[{(\[Lambda] \[Alpha] + \[Lambda] \[Mu] y) (p - \[Theta] \
x^2 - (1 - \[Theta]) y^2 - b - d) + (a - 
        k p + \[Lambda] (\[Alpha] x + (1 - \[Alpha]) y + \[Lambda] \
\[Mu] y)) (-2 \[Theta] x) == 
    0, (\[Lambda] (1 - \[Alpha]) + \[Lambda] \[Mu] x) (p - \[Theta] \
x^2 - (1 - \[Theta]) y^2 - b - d) + (a - 
        k p + \[Lambda] (\[Alpha] x + (1 - \[Alpha]) y + \[Lambda] \
\[Mu] y)) (-2 (1 - \[Theta]) y) == 0}, {x, -1, 1}, {y, -1, 1}],
 {\[Lambda], -1, 1}, {\[Alpha], -1, 1}, {\[Mu], -1, 1}, {p, -1, 
  1}, {\[Theta], -1, 1}, {b, -1, 1}, {d, -1, 1}, {a, -1, 1}, {k, -1, 
  1}]

Added code and the .nb file. Thanks.

Solve[{(? ? + ? ? y) (p - ? x^2 - (1 - ?) y^2 - b - d) + 
(a - k p + ? (? x + (1 - ?) y + ? ? y)) (-2 ? x) == 0, 
(? (1 - ?) + ? ? x) (p - ? x^2 - (1 - ?) y^2 - b - d) + 
(a - k p + ? (? x + (1 - ?) y + ? ? y)) (-2 (1 - ?) y) == 0}, {x, y}]

Attachments: