In need of mathematica or maple

[msmith12]

so, this is probably not exactly posted in the right place, but I was wondering if someone could enter a couple of things into a math program for me. I have two simple systems of equations and need the values for them, and unfortunately, don't have mathematica on this computer, and I started working these with pencil and paper, and they did not look very pretty... so without further adiou...

$$(1-a-b)(1+4x+3y)=a(4-4x-y)=b(2+y)$$
$$(1-x-y)(1+6a-b)=x(4-2a+8b)=y(6-5a-6b)$$

and...

$$a(1+4x+3y)=b(4-4x-y)$$
$$x(4a+2b)=y(6a+b)=(1-x-y)(a+7b)$$

i need to find the values of a,b,x,y for each set of equations.

(in case you were wondering where these came from, they are the equilibrium probabilites that player A chooses 1,2,3 and player B chooses a,b,c)

thanks a bunch

~tired of number crunching

 

[LakeMountD]

so, this is probably not exactly posted in the right place, but I was wondering if someone could enter a couple of things into a math program for me. I have two simple systems of equations and need the values for them, and unfortunately, don't have mathematica on this computer, and I started working these with pencil and paper, and they did not look very pretty... so without further adiou...

$$(1-a-b)(1+4x+3y)=a(4-4x-y)=b(2+y)$$
$$(1-x-y)(1+6a-b)=x(4-2a+8b)=y(6-5a-6b)$$

and...

$$a(1+4x+3y)=b(4-4x-y)$$
$$x(4a+2b)=y(6a+b)=(1-x-y)(a+7b)$$

i need to find the values of a,b,x,y for each set of equations.

(in case you were wondering where these came from, they are the equilibrium probabilites that player A chooses 1,2,3 and player B chooses a,b,c)

thanks a bunch

~tired of number crunching

if you can show me exactly how i enter it into maple i will do it for you.. i have maple 8.. I am not quite sure how to do it when there is two equal signs in the equation like that.

 

[msmith12]

I am not exactly positive, but it should work to split up the three equals signs into two different equalities... so the command should work something like...

sys1:={(1-a-b)(1+4x+3y)=a(4-4x-y),a(4-4x-y)=b(2+y),(1-x-y)(1-6a-b)=x(4-2a+8b),x(4-2a+8b)=y(6-5a-6b)};
ans1:=solve(sys1);
sys2:={a(1+4x+3y)=b(4-4x-y),x(4a+2b)=y(6a+b),y(6a+b)=(1-x-y)(a+7b)};
ans2:=solve(sys2);

hopefully that will work... if not, hopefully i just missed a comma... if anyone who is reading this can provide any insight, I would be much obliged...

thanks

 

[Edgardo]

I typed it in Mathematica and get the following:

System 1:
{{x -> 1.70045, a -> 1.3017, b -> 0.865607, y -> -2.48157},
{x -> 0., a -> 0., b -> 1., y -> -2.},
{x -> 0.100997, a -> 0.0937245, b -> 1.05555, y -> -1.54364},
{x -> 0.154481, a -> 0.314785, b -> 0.375722, y -> 0.453553},
{x -> 1.09427, a -> 1.26404, b -> -0.192182, y -> -0.0861005},
{x -> -0.452824, a -> -0.232922, b -> -0.661729, y -> 0.0336715}}

Note: In your original post, you wrote: (1+6a-b). The above solution
is for (1+6a-b)

In your second post, you wrote: (1-6a-b). In this case Mathematica gives:

{{x -> 1.51463, a -> 1.46436, b -> -1.07928, y -> -2.22261},
{x -> 0., a -> 0., b -> 1., y -> -2.},
{x -> 0.361879, a -> 0.614746, b -> 0.252376, y -> 1.22748},
{x -> -0.957595, a -> -0.703093, b -> -2.07493, y -> 0.487984},
{x -> 1.10136, a -> 1.26672, b -> -0.194326, y -> -0.116498},
{x -> -0.011296, a -> 0.132274, b -> 0.271161, y -> -0.0179704}}


For the second set of equations, you only gave 3 equations.

 

[LakeMountD]

maple 8 must be a lot different from mathematica becuase it gave me this


sys1 := {1 - x(1 - 6 a - b) - y(1 - 6 a - b) = x (4 - 2 a + 8 b),

(1 - a - b) (1 + 4 x + 3 y) = a (4 - 4 x - y),

a(4 - 4 x - y) = b (2 + y),

x (4 - 2 a + 8 b) = y (6 - 5 a - 6 b)}

ans1 :=


sys2 := {a (1 + 4 x + 3 y) = b (4 - 4 x - y),

x (4 a + 2 b) = y (6 a + b),

y (6 a + b) = 1 - x(a + 7 b) - y(a + 7 b)}


ans2 :=
as your answer