SOLUTION: Solve the system of equations. {{{3j^2 + 17j + 8k - 84 = 0}}} {{{-j + 8k - 63 = 0}}} j:___, k:___ and j:___, k:___

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Solve the system of equations. {{{3j^2 + 17j + 8k - 84 = 0}}} {{{-j + 8k - 63 = 0}}} j:___, k:___ and j:___, k:___      Log On


   

Question 876476: Solve the system of equations.
3j%5E2+%2B+17j+%2B+8k+-+84+=+0
-j+%2B+8k+-+63+=+0
j:___, k:___
and
j:___, k:___
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
3j%5E2+%2B+17j+%2B+8k+-+84+=+0
-j+%2B+8k+-+63+=+0
Subtract the 2nd equation from the first equation
3j%5E2+%2B+17j+%2B+8k+-+84+=+0
+0++-+j+%2B++8k+++-+63+=+0
---------------------------------subtraction eliminates k
3j^2 + 18j + 0 - 21 = 0
A quadratic we can factor
(3j - 3)(j + 7) = 0
3j = 3
j = 1
and
j = -7
:
Use the 2nd equation to find k
when j = 1
-1 + 8k - 63 = 0
8k = 63 + 1
k = 8, when j = 1
:
When j= -7
7 + 8k - 63 = 0
8k = 63 - 7
k = 56/8
k = 7 when j = -7
:
:
Check solutions in 1st equation
j=1, k=8
3(1^2) + 17(1) + 8(8) - 84 = 0
3 + 17 + 64 - 84 = 0
j=-7, k=7
3(-7^2) + 17(-7) + 8(7) - 84 = 0
147 - 119 + 56 - 84 = 0