Solve the system of linear inequalities with parameters (*) { 0 ≤ − 2 x + 2 y − 3 b + 3 a ≤ 2 0 ≤ − 2 x − 3 y + 6 b + 3 a ≤ 1 0 ≤ x ≤ 1 0 ≤ y ≤ 2 0 ≤ a ≤ 1 0 ≤ b ≤ 1 Here x,y are unknown variables and a,b are parameters.My attempt. By adding the inequalities with some coeficients I separated the variables and get the simple system (**) { 0 ≤ y + 6 a ≤ 5 , 0 ≤ − x + 9 a + 3 b ≤ 8. and I am able to solve it. But the solutions of the last system are not solution of the initial system!Maple and wolframAlpha cant solve the system.P.S.1 For a = 63 100 and b = 59 100 Maple gives the solutions { x = 1 , 9 50 ≤ y , y ≤ 11 25 } , { x = − 3 / 2 y + 127 100 , 9 50 &lt; y , y &lt; 11 25 } , { 9 50 &lt; y , x &lt; 1 , y &lt; 11 25 , − 3 / 2 y + 127 100 &lt; x } , { y = 11 25 , 61 100 ≤ x , x &lt; 1 } , { x = − 3 / 2 y + 127 100 , 11 25 &lt; y , y &lt; 127 150 } , { 11 25 &lt; y , x &lt; − 2 y + 47 25 , y &lt; 127 150 , − 3 / 2 y + 127 100 &lt; x } , { x = − 2 y + 47 25 , 11 25 &lt; y , y &lt; 127 150 } , { x = 0 , 127 150 ≤ y , y ≤ 47 50 } , { y = 127 150 , x ≤ 14 75 , 0 &lt; x } , { 0 &lt; x , 127 150 &lt; y , x &lt; − 2 y + 47 25 , y &lt; 47 50 } , { x = − 2 y + 47 25 , 127 150 &lt; y , y &lt; 47 50 }

Question

Solve the system of linear inequalities with parameters                    (*)                              {                                                    0                ≤                                                −                  2                                                  x                +                2                                y                −                3                                b                +                3                                a                ≤                2                                                                    0                ≤                −                2                                x                −                3                                y                +                6                                b                                                                  +                  3                  a                                                                    ≤                1                                                                    0                ≤                x                ≤                1                                                                    0                ≤                y                ≤                2                                                                    0                ≤                a                ≤                1                                                                    0                ≤                b                ≤                1                                                                  Here x,y are unknown variables and a,b are parameters.My attempt. By adding the inequalities with some coeficients I separated the variables and get the simple system                    (**)                              {                                                    0                ≤                y                +                6                a                ≤                5                ,                                                                    0                ≤                −                x                +                9                a                +                3                b                ≤                8.                                                                  and I am able to solve it. But the solutions of the last system are not solution of the initial system!Maple and wolframAlpha cant solve the system.P.S.1 For   a  =      63    100   and   b  =      59    100   Maple gives the solutions                              {          x          =          1          ,                              9            50                    ≤          y          ,          y          ≤                              11            25                    }                ,                  {          x          =          −          3                  /          2                    y          +                              127            100                    ,                              9            50                    &amp;lt;          y          ,          y          &amp;lt;                              11            25                    }                ,                  {                              9            50                    &amp;lt;          y          ,          x          &amp;lt;          1          ,          y          &amp;lt;                              11            25                    ,          −          3                  /          2                    y          +                              127            100                    &amp;lt;          x          }                ,                  {          y          =                              11            25                    ,                              61            100                    ≤          x          ,          x          &amp;lt;          1          }                ,                  {          x          =          −          3                  /          2                    y          +                              127            100                    ,                              11            25                    &amp;lt;          y          ,          y          &amp;lt;                              127            150                    }                ,                  {                              11            25                    &amp;lt;          y          ,          x          &amp;lt;          −          2                    y          +                              47            25                    ,          y          &amp;lt;                              127            150                    ,          −          3                  /          2                    y          +                              127            100                    &amp;lt;          x          }                ,                  {          x          =          −          2                    y          +                              47            25                    ,                              11            25                    &amp;lt;          y          ,          y          &amp;lt;                              127            150                    }                ,                  {          x          =          0          ,                              127            150                    ≤          y          ,          y          ≤                              47            50                    }                ,                  {          y          =                              127            150                    ,          x          ≤                              14            75                    ,          0          &amp;lt;          x          }                ,                  {          0          &amp;lt;          x          ,                              127            150                    &amp;lt;          y          ,          x          &amp;lt;          −          2                    y          +                              47            25                    ,          y          &amp;lt;                              47            50                    }                ,                                      {          x          =          −          2                    y          +                              47            25                    ,                              127            150                    &amp;lt;          y          ,          y          &amp;lt;                              47            50                    }

Cristopher Barrera · Accepted Answer

9  a  +  3  b  −  8  ≤  x  ≤  9  a  +  3  b  −  6  a  ≤  y  ≤  5  −  6  aThese are the equations, and there are constraints  0  ≤  x  ≤  1  0  ≤  y  ≤  2  0  ≤  a  ≤  1  0  ≤  b  ≤  1The intersect can exist or not depending to a and b.

Emmy Knox · Accepted Answer

Yours system has no solutions. In fact      {                            y          ≤          5          −          6          a          ,                                      y          ≤          2                            ⟹    a  ≥      1    2  .But then   x  ≤  9  a  +  3  b  ≤      9    2    +  3  b    ⟹    x  &amp;gt;      9    2    &amp;gt;  1 but must be   x  ≤  1.

Solve the system of linear inequalities with parameters <mtable displaystyle="true"> <mlabel

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