SOLUTION: solve sysyem of three equation 2x+y-z=10 6x+5y-2z=23 3x-y+z=5 please show all work

Question 631610: solve sysyem of three equation
2x+y-z=10
6x+5y-2z=23
3x-y+z=5
please show all work
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
2x+y-z=10................(1)
6x+5y-2z=23..............(2)
3x-y+z=5.................(3)

Multiply (1) by -2 and add to (2)
-4x-2y+2z=-20
6x+5y-2z=23
------------------
2x+3y=3.....................(4)

Multiply (3) by 2 and add to (2)
6x+5y-2z=23
6x-2y+2z=10
---------------
12x+3y=33
3(4x+y)=33
3(4x+y)/3=33/3
4x+y=11....................(5)

Multiply (5)by -3 and add to (4)
2x+3y=3
-12x-3y=-33
------------------
-10x=-30
-10x/-10=-30/-10
x=3

Put the value of x in (5)
4x+y=11....................(5)
4(3)+y=11
12+y=11
y=11-12
y=-1
Put the value of x and y in (3)
3x-y+z=5.................(3)
3(3)-(-1)+z=5
9+1+z=5
10+z=5
z=5-10
z=-5

x,y,z=3,-1,-5

Check
======
Put the values of x,y,z in (1)
2x+y-z=10................(1)
2(3)+(-1)-(-5)=10
6-1+5=10
5+5=10
10=10

Put the values of x,y,z in (2)
6x+5y-2z=23..............(2)
6(3)+5(-1)-2(-5)=23
18-5+10=23
13+10=23
23=23

Put the values of x,y,z in (3)
3x-y+z=5.................(3)
3(3)-(-1)+(-5)=5
9+1-5=5
10-5=5
5=5

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