SOLUTION: the linear system has the solution (a,b,2) 2x-y-z=-3 x+2y-2z=-2 x+ky+z=5 determine the values of a,b and k

Question 332481: the linear system has the solution (a,b,2)
2x-y-z=-3
x+2y-2z=-2
x+ky+z=5
determine the values of a,b and k
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the linear system has the solution (a,b,2)
2x - y - z = -3
x +2y -2z =-2
x +ky + z = 5
determine the values of a,b and k
rewrite each equation replacing z with 2, replace x & y with a and b
2a - b - 2 = -3
2a - b = -3 + 2
2a - b = -1
:
a + 2b - 2(2) = -2
a + 2b = -2 + 4
a + 2b = 2
:
a + bk + 2 = 5
a + bk = 5 - 2
a + bk = 3
:
Find b, multiply the 2nd equation by 2, subtract the 1st equation
2a + 4b = 4
2a - b = -1
------------------eliminates a, find b
5b = 5
b = 1
:
Find a using, a + 2b = 2
a + 2(1) = 2
a = 2 - 2
a = 0
:
Find k using the 3rd equation
a + bk = 3
0 + 1k = 3
k = 3
:
Summarize: a=0, b=1, k=3
:
You can confirm these solutions in the original equations
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