For which value(s) of parameter m is there a solution for this system { m x + y = m m x + 2 y = 1 2 x + m y = m + 1 when does this system of equations have a solution?

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For which value(s) of parameter m is there a solution for this system      {                            m          x          +          y          =          m                                      m          x          +          2          y          =          1                                      2          x          +          m          y          =          m          +          1                        when does this system of equations have a solution?

ryancameron52 · Accepted Answer

Compute the values of   x and   y dependent on   m for the following system, then solve   2  x  +  m  y  =  m  +  1 (the last equation) to find the values of parameter   m for   x and   y:      {                            m          x          +          y          =          m                                      m          x          +          2          y          =          1                        So,      {                            2          m          x          +          2          y          =          2          m                                      m          x          +          2          y          =          1                        Subtracting two equations, will have:  m  x  =  2  m  −  1- If   m  ≠  0, we may divide by   m and get   x  =  (  2  m  −  1  )  /  m and   y  =  1  −  m.- If   m  =  0, the system has no solution.Putting   x and   y in the last equation   m  ≠  0, we&#039;ll have:      m    3    −  3  m  +  2  =  0  (      m    3    −  1  )  −  3  m  +  3  =  0  (  m  −  1  )  (      m    2    +  m  +  1  )  −  3  (  m  −  1  )  =  0  (  m  −  1  )  (      m    2    +  m  −  2  )  =  0Thus the values of parameter   m are   m  =  1 or   m  =  −  2.

ownerweneuf · Accepted Answer

Comment to expert&#039;s answer. Be careful: If   m  =  0 then the equation   m  x  =  2  m  −  1 gives you   0  =  −  1, so you have no solution. Ruling out this case you have   x  =            2      m      −      1        m   or   (  2  m  −  1  )  /  m which is not th esame as   2  m  −  1  /  m.

For which value(s) of parameter m is there a solution for this system { <mtable columna

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