SOLUTION: solve the system: 5x-3y+z=-7 4x+5y+3z=-2 2x-3y+5z=22 show work and i think you can solve it in the calculator by matrices right? if you know both ways please show thanks!

Question 164189: solve the system:
5x-3y+z=-7
4x+5y+3z=-2
2x-3y+5z=22
show work and i think you can solve it in the calculator by matrices right?
if you know both ways please show thanks!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve the system:
5x-3y+z=-7
4x+5y+3z=-2
2x-3y+5z=22
show work and i think you can solve it in the calculator by matrices right?
if you know both ways please show thanks!
-------------------
You can do it by elimination and substitution, but that's tedious and error prone.
If you calculator has the functionality, you can do a matrix solution on it.
I have an Excel sheet that does it using determinants.
By Excel:
x = -3
y = -1
z = +5
-----------
Using elimination and substitution:
5x-3y+z=-7 eqn 1
4x+5y+3z=-2 eqn 2
2x-3y+5z=22 eqn 3
------------
Eqn 1 has a z coeff of 1, so muliply it by 3, and then by 5.
5x-3y+z=-7
15x - 9y + 3z = -21 eqn 1 times 3
4x + 5y + 3z = -2 eqn 2
11x - 14y = -19 Subtract eqn 2
----------------
5x-3y+z=-7 eqn 1 again
25x - 15y + 5z = -35 eqn 1 times 5
2x - 3y + 5z = 22 eqn 3
23x - 12y = -57 Subract eqn 3
-------------
Now there are 2 eqns in 2 unknowns (x and y)
11x - 14y = -19
23x - 12y = -57
Multiply the 1st times 6, and the 2nd times 7 to get the same coeff for y.
66x - 84y = -114
161x -84y = -399 Subtract
-95x = 285
x = -3
------------
Sub into 11x - 14y = -19 to get
y = -1
-----------
Sub x and y into any of the original 3 eqns to get
z = +5

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