SOLUTION: x-y-2z=4 -x+2y+z=1 -x+y-3z=11

Question 1104814: x-y-2z=4
-x+2y+z=1
-x+y-3z=11
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) x -y -2z = 4
:
2) -x + 2y +z =1
:
3) -x +y -3z = 11
:
add equations 1 and 3
:
4) -5z = 15
:
solve equation 4 for z
:
z = -3
:
substitute for z in equations 1 and 2
:
x -y -2(-3) = 4
:
5) x -y = -2
:
-x +2y -3 = 1
:
6) -x +2y = 4
:
add equations 5 and 6
:
y = 2
:
so far we have y = 2 and z = -3
:
substitute for y and z in equation 1
:
x -2 -2(-3) = 4
:
x = 0
:
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we have x=0, y=2 and z=-3
:
check our answer by substituting for x, y, z in equations 1, 2, 3
:
1) 0 -2 -2(-3) = 4
4 = 4
:
2) -0 + 2(2) +(-3) = 1
1 = 1
:
3) -0 +2 -3(-3) = 11
11 = 11
:
our answer checks
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