SOLUTION: solve 2x-y+z=-7, x-3y+4z=-19, and -x+4y-3z=18 can someone show how they got the answer please, ty

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Question 626982: solve 2x-y+z=-7, x-3y+4z=-19, and -x+4y-3z=18
can someone show how they got the answer please, ty
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

solve by finding the value of 4 matrices

2x- y+ z=-7, 

 x-3y+4z=-19, 

-x+4y-3z=18

A=%28matrix%283%2C3%2Ca1%2Cb1%2Cc1%2Ca2%2Cb2%2Cc2%2Ca3%2Cb3%2Cc3%29%29  |A|=  a1(b2c3-c2b3) - b1(a2c3-c2a3) + c1(a2b3-b2a3) 

%28matrix%283%2C3%2C2%2C-1%2C1%2C1%2C-3%2C4%2C-1%2C4%2C-3%29%29 = -12



%28matrix%283%2C3%2C-7%2C-1%2C1%2C-19%2C-3%2C4%2C18%2C4%2C-3%29%29 = 12   x = 12%2F%28-12%29+=+-1

%28matrix%283%2C3%2C2%2C-7%2C1%2C1%2C-19%2C4%2C-1%2C18%2C-3%29%29 = -24   y = %28-24%29%2F%28-12%29+=+2

%28matrix%283%2C3%2C2%2C-1%2C-7%2C1%2C-3%2C-19%2C-1%2C4%2C18%29%29 = 36   z = 36%2F%28-12%29+=+-3

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve
2x-y+z=-7
x-3y+4z=-19
-x+4y-3z=18
----------------
Rearrange the equations
x-3y+4z = -19
-x+4y-3z= 18
2x-y+z = -7
------
Add 1st to 2nd
Subtract 2 times 1 from 3rd to get:
x - 3y + 4z = -19
0 + y + z = -1
0 + 5y - 7z = 41
--------------------
Subtract 5 times 2nd from 3rd to get:
x - 3y + 4z = -19
0 + y + z = -1
0 + 0 - 12z = 36
---------------------
Solve the 3rd equation for "z":
z = -3
-----
Substitute z = -3 into the 2nd equation
and solve for "y":
y = 2
----
Substitute z = -3 and y = 2 into the 1st equation
and solve for "x":
x -3*2 + 4*-3 = -19
x -6 -12 = -19
x = -1
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Cheers,
Stan H.
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