solve multiple equation in one variable

syms p1 p2 p3 p4 p5

B = [(75*p2)/2 - (153*p3)/4 + (199*p4)/6 + (31*p5)/12 - 2165/12 == -433/36, 58*p2 - (89*p3)/2 + (457*p4)/9 + (127*p5)/18 - 4763/18 == -433/36, 38*p2 - (59*p3)/2 + (344*p4)/9 + (161*p5)/18 - 3031/18 == -433/36, 70*p2 - 81*p3 + (625*p4)/9 + (125*p5)/9 - 3031/9 == -433/36, (89*p2)/2 - (225*p3)/4 + (841*p4)/18 - (11*p5)/36 - 9959/36 == -433/36]

solve(b)

solx = [ans.p2 ans.p3 ans.p4 ans.p5]

i got 5 equation in B variable but when im trying to solve it. it always show

p2 = [0x1 sym]

p3 = [0x1 sym]

p4 = [0x1 sym]

p5 = [0x1 sym]

empty sym; 0 - by-4

is there any solution to solve that equation?

thank you

Answer 1

[Davide Masiello]

I think the problem is that you have 5 equations and 4 variables, because p1 does not appear anywhere in the system.

Therefore the system is overdetermined.

If I try to solve canceling the last equation it works, see below

syms p1 p2 p3 p4 p5
B = [(75*p2)/2 - (153*p3)/4 + (199*p4)/6 + (31*p5)/12 - 2165/12 == -433/36; 58*p2 - (89*p3)/2 + (457*p4)/9 + (127*p5)/18 - 4763/18 == -433/36; 38*p2 - (59*p3)/2 + (344*p4)/9 + (161*p5)/18 - 3031/18 == -433/36; 70*p2 - 81*p3 + (625*p4)/9 + (125*p5)/9 - 3031/9 == -433/36] % (89*p2)/2 - (225*p3)/4 + (841*p4)/18 - (11*p5)/36 - 9959/36 == -433/36]

B = 

s = solve(B)

s = struct with fields:
    p2: 122537701/16461144
    p3: -1231019/783864
    p4: -1665751/304836
    p5: 7365763/1829016

Are you sure the system is correctly coded?

You might have missed to include p1 somewhere.

[Kalvin]

I see. So is there any command that can erase 1 equation from that variable? The p1 is missing because i need to substitude the p1 with another equation. Thats why i need to erase one equation from that variable.

[Torsten]

syms p1 p2 p3 p4 p5
B = [(75*p2)/2 - (153*p3)/4 + (199*p4)/6 + (31*p5)/12 - 2165/12 == -433/36, 58*p2 - (89*p3)/2 + (457*p4)/9 + (127*p5)/18 - 4763/18 == -433/36, 38*p2 - (59*p3)/2 + (344*p4)/9 + (161*p5)/18 - 3031/18 == -433/36, 70*p2 - 81*p3 + (625*p4)/9 + (125*p5)/9 - 3031/9 == -433/36, (89*p2)/2 - (225*p3)/4 + (841*p4)/18 - (11*p5)/36 - 9959/36 == -433/36]

B = 

s = solve([B(1),B(3),B(4),B(5)]);  % e.g.
p2 = double(s.p2)

p2 = -0.9168

p3 = double(s.p3)

p3 = -1.1433

p4 = double(s.p4)

p4 = 5.1320

p5 = double(s.p5)

p5 = -4.3249

or use

[A,b] = equationsToMatrix(B);
sol = double(A)\double(b)

sol = 4×1

0.8276 -0.6442 4.0401 -4.8917

which solves the system of 5 equations in 4 unknowns in the least-squares sense.