how to find specific variable values for solving equation system

Hello,i have the following equation system.

is there a way in matlab to find P1..P6 values so

pr(2)=pr(1)+5

pr(3)=pr(2)+5

etc..

x1=10;
pr(1)=x1-p1-p5-p6;
pr(2)=x1+p1-p5-p6;
pr(3)=x1-p2+p5-p6;
pr(4)=x1+p2+p5-p6;
pr(5)=x1-p3+p6;
pr(6)=x1-p4+p3+p6;
pr(7)=x1+p4+p3+p6;

Answer 1

[Torsten]

Yes.

You have 13 linear equations for 13 unknowns P = [pr(1),...,pr(7),p1,...,p6].

Write the system as

A*P = B

and solve for P as

P = A\B

In your case:

x1 = 10;
A = [1 0 0 0 0 0 0 1 0 0 0 1 1;...
     0 1 0 0 0 0 0 -1 0 0 0 1 1;...
     0 0 1 0 0 0 0 0 1 0 0 -1 1;...
     0 0 0 1 0 0 0 0 -1 0 0 -1 1;...
     0 0 0 0 1 0 0 0 0 1 0 0 -1;...
     0 0 0 0 0 1 0 0 0 -1 1 0 -1;...
     0 0 0 0 0 0 1 0 0 -1 -1 0 -1;...
     -1 1 0 0 0 0 0 0 0 0 0 0 0;...
     0 -1 1 0 0 0 0 0 0 0 0 0 0;...
     0 0 -1 1 0 0 0 0 0 0 0 0 0;...
     0 0 0 -1 1 0 0 0 0 0 0 0 0;...
     0 0 0 0 -1 1 0 0 0 0 0 0 0;...
     0 0 0 0 0 -1 1 0 0 0 0 0 0];
B = [x1 ; x1 ; x1 ; x1 ; x1 ; x1; x1 ; 5 ; 5 ; 5 ; 5 ; 5 ; 5];
P = A\B

[fima v]

Hello i need d1 d2 d3 d4 d5 d6 to be 5

how do i formulate the matrices method you proposed?

so i get p1 p3 p6 p4 such values that will do d1..d6=5

x1=10;
p1=2.5;
p5=5;
p6=10;
p3=3.75;
p4=+2.5;
pr(1)=x1-p1-p5-p6;
pr(2)=x1+p1-p5-p6;
pr(3)=x1-p1+p5-p6;
pr(4)=x1+p1+p5-p6;
pr(5)=x1-p3+p6;
pr(6)=x1-p4+p3+p6;
pr(7)=x1+p4+p3+p6;
d1=pr(2)-pr(1)
d2=pr(3)-pr(2)
d3=pr(4)-pr(3)
d4=pr(5)-pr(4)
d5=pr(6)-pr(5)
d6=pr(7)-pr(6)

[Torsten]

I already defined the matrix equation above and determined the solution vector

P = [pr(1);pr(2);pr(3);pr(4);pr(5);pr(6);pr(7);p1;p2;p3;p4;p5;p6]