find value of x, y and z, if x+y=30 and y+z=18 and x+z=13

Question

find value of x, y and z, if x+y=30 and y+z=18 and x+z=13

Answer 1

(Note to tutors:  If teachers would teach the elimination method more often, then matrix manipulation would be easier to learn later.)

 

There are 3 equations in 3 unknowns (very important, that means that we can solve for x, y, z).  The equations can be written this way:

  x  +  y           =  30     (eq1)

          y  +  z   =  18     (eq2)

  x          +  z   =  13     (eq3)

 

To solve for x, subtract eq2 from eq1, then add eq3

  x  +  y           =  30

          y  +  z   =  18

 -----------------------

  x          -   z   =  12

  x         +   z   =  13

 -----------------------

 2x                  =  25

   x                  = 12.5

 

To solve for y, subtract eq3 from eq2, then add eq1:

        2y           =  35

          y           = 17.5

 

To solve for z, subtract eq1 from eq3, then add eq2:

               2z     = (-17) + 18

                 z     = 0.5

 

Answer 2

x + y = 30

y + z = 18

x + z = 13

 

We can take any of the equations and solve for one variable in terms of another

and then use substitution.  I chose to take the 2nd equation and solve for y

y+z = 18

y = 18-z

 

Substitute 18-z in place of y in equation 1

 

x + 18 - z = 30

x -z = 12

 

We now have two equations that have only x and z variables

 

x - z = 12

x + z =13        add the equations to eliminate z

-------------

2x = 25

x = 25/2

x = 12.5

 

x + z =13 and x = 12.5 so

12.5 + z = 13

z = 13 - 12.5

z = 0.5

 

y = 18 - z

y = 18 - 0.5

y = 17.5

 

Our answers are x=12.5, y = 17.5, z = 0.5

 

Check:  x + y = 30           y+z=18             x+z=13

           12.5+17.5=30      17.5+0.5=18     12.5+0.5=13

           30 = 30                18 = 18             13=13

 

Our answer satisfies all given conditions