Solving a system of three equations: d = s ⋅ 3 , c = s ⋅ 1.5 , c = 2 ⋅ d.

Question

Solving a system of three equations:   d  =  s  ⋅  3  ,  c  =  s  ⋅  1.5  ,  c  =  2  ⋅  d.

trestegp0 · Accepted Answer

If I gave you a system of two equations in two unknowns,

u = v, 3 u = 3 v,

you would correctly answer that they could be anything, as long as they were the same.
If I switched to

x = y, x = 5 y

you would be right to be suspicious. Indeed, we get

5 y = y,

then subtract 𝑦 from both sides,

4 y = 0,

so

y = 0

and

x = 0.

.

w = 3 u, v = 1.5 u, w = 2 v,

,
which has infinitely many solutions, as long as the ratios are maintained, for example

(u = 2, v = 3, w = 6),

, or

(u = 22, v = 33, w = 66) .

However, as the others have pointed out, your system is of the inconsistent ratio type, the only answer is all equal to

0.

If the third equation of your system were switched to

d = 2 c

you would get infinitely many solutions.

Spactapsula2l · Accepted Answer

Since   c  =  2  d and   c  =  1.5  s, we have   2  d  =  1.5  s, so   2  (  3  s  )                    =                    (        1        )              1.5  s since   d  =  3  s. Now   6  s  =  1.5  s by   (  1  ), which can only happen if   s  =  0. Thus   s  =  d  =  c  =  0.

Solving a system of three equations: d=s⋅3,c=s⋅1.5,c=2⋅d.

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