SOLUTION: 2 x - y + z = 9 3 x -5 y + 4 z = 30 5 x + y -2 z = 4 please show work, so i can understand how to do it. thank you

Question 247356: 2 x - y + z = 9
3 x -5 y + 4 z = 30
5 x + y -2 z = 4

please show work, so i can understand how to do it. thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
2 x - y + z = 9
3 x -5 y + 4 z = 30
5 x + y -2 z = 4
-----------------------
Subtract 1st Eq for 2nd to get:
2 x - y + z = 9
x -4 y + 3 z = 21
5 x + y -2 z = 4
-------------------------------
Make the 2nd Equation the 1st:
x - 4y + 3 z = 21
2x - y + z = 9
5x + y -2 z = 4
-------------------------------
Subtract 2 times 1st from 2nd
Subtract 5 times 1st from 3rd to get
x - 4y + 3 z = 21
0x + 7y -5z = -33
0x +21y -17z = -101
-------------------------------
Subtract 3 times 2nd from the 3rd to get:
x - 4y + 3 z = 21
0x + 7y -5z = -33
0x + 0y -2z = -2
----------------------
Solve 3rd for "z" : z = 1
----------------------
Substitute z=1 into 2nd Eq. and solve for "y":
7y - 5 = -33
7y = -28
y = -4
----------------------
Substitute z = 1 and y = -4 into the 1st Eq and solve for "x.
x -4*-4 + 3*1 = 21
x + 16 + 3 = 21
x + 19 = 21
x = 2
---------------------
Final solution:
x = 2
y = -4
z = 1
=================
Cheers,
Stan H.

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