Solution - Linear equations with two unknowns

System of Linear Equations entered :

   [1]    z + g = 50
   [2]    2z + 3g = 40

Graphic Representation of the Equations :

    g + z = 50        3g + 2z = 40  

  
 

Solve by Substitution :

// Solve equation [1] for the variable  g 
 

  [1]    g = -z + 50

// Plug this in for variable  g  in equation [2]

   [2]    2z + 3•(-z +50) = 40
   [2]    -z = -110

// Solve equation [2] for the variable  z 

   [2]    z = 110 

// By now we know this much :

    z = 110
    g = -z+50

// Use the  z  value to solve for  g 

    g = -(110)+50 = -60 

Solution :

 {z,g} = {110,-60}