SOLUTION: Please help! Tell whether the given ordered triple is a solution of the system. 1) (5, -2, 2) 2x-y+z=5 x+2y-z=-1 -2x+y-3z=-15 2) (1, -1, 3) 4x+2y+3z=11 x-2y+z=6

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Please help! Tell whether the given ordered triple is a solution of the system. 1) (5, -2, 2) 2x-y+z=5 x+2y-z=-1 -2x+y-3z=-15 2) (1, -1, 3) 4x+2y+3z=11 x-2y+z=6      Log On


   

Question 146537: Please help!
Tell whether the given ordered triple is a solution of the system.
1) (5, -2, 2)
2x-y+z=5
x+2y-z=-1
-2x+y-3z=-15



2) (1, -1, 3)
4x+2y+3z=11
x-2y+z=6
2x+y+2z=7
Thanks so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1)
------------------ Let's test the first equation ------------------
2x-y%2Bz=5 Start with the first equation.


2%2A%285%29-%28-2%29%2B%282%29=5 Plug in x=5, y=-2, and z=2.


14=5 Evaluate and simplify the left side.


Since the equation is not true, this means that (5, -2, 2) is not a solution to the system. Remember, a solution has to satisfy all of the equations in the system.




2)
------------------ Let's test the first equation ------------------


4x%2B2y%2B3z=11 Start with the first equation.


4%2A%281%29%2B2%2A%28-1%29%2B3%2A%283%29=11 Plug in x=1, y=-1, and z=3.


11=11 Evaluate and simplify the left side.

Notice how the equation is true.

------------------ Now let's test the second equation ------------------


x-2y%2Bz=6 Start with the second equation.


%281%29-2%2A%28-1%29%2B%283%29=6 Plug in x=1, y=-1, and z=3.


6=6 Evaluate and simplify the left side.

Notice how the equation is true.

------------------ Now let's test the third equation ------------------


2x%2By%2B2z=7 Start with the third equation.


2%2A%281%29%2B%28-1%29%2B2%2A%283%29=7 Plug in x=1, y=-1, and z=3.


7=7 Evaluate and simplify the left side.

Notice how the equation is true.




Since all of the equations in the system are true, this means that (1, -1, 3) is a solution.