Write an example of a system of three equations in three variables that has (3, 5, 2) as a solution. Show that the ordered triple satisfies all three equations.

Question

Write an example of a system of three equations in three variables that has (­3, 5, 2) as a solution. Show that the ordered triple satisfies all three equations.

solomonzelman · Answer

You can do it backwards :)

solomonzelman · Answer

$\color{#000000}{    \displaystyle   2(3)-(5)+2(2)=5          }$
$\color{#000000}{    \displaystyle   (3)+(5)-(2)=6        }$
$\color{#000000}{    \displaystyle   6(3)-2(5)-3(2)=2        }$

$\color{#000000}{    \displaystyle   2x-y+2z=5          }$
$\color{#000000}{    \displaystyle   x+y-z=6        }$
$\color{#000000}{    \displaystyle   6x-2y-3z=2        }$

and clearly,  $\color{#000000}{    \displaystyle  (x,y,z)=(3,5,2)         }$  is a solution.

solomonzelman · Answer

See what I am doing?

anonymous · Answer

Ah yes! I had come up with something different (with the solutions 3, 5, and 2 but the results just being 0) but this makes a lot more sense. Thank you!

solomonzelman · Answer

Yeah, when you are asked to come up with a system that has a particular solution, you can always go becwards like this.

solomonzelman · Answer

(( You can also tell that there is an infinite number of possible sustems that would satisfy a particular solution. ))

solomonzelman · Answer

In any case, you welcome:)