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**Unformatted text preview: **lama pen in 45 minutes. On his own,
Daniel can clean the pen in an hour. How long does it take Donnie to clean the llama pen on
his own?
8. A certain bacteria culture follows the Law of Uninbited Growth, Equation 6.4. After 10
minutes, there are 10,000 bacteria. Five minutes later, there are 14,000 bacteria. How many
bacteria were present initially? How long before there are 50,000 bacteria? 8.7 Systems of Non-Linear Equations and Inequalities 545 9. Consider the system of nonlinear equations below 4+3 = 1 xy
3 2
+ = −1
xy
If we let u = 1
x and v = 1
y then the system becomes
4u + 3 v =
1
3u + 2v = −1 This associated system of linear equations can then be solved using any of the techniques
1
presented earlier in the chapter to ﬁnd that u = −5 and v = 7. Thus x = u = − 1 and
5
1
1
y = v = 7.
We say that the original system is linear in form because its equations are not linear but a
few basic substitutions reveal a structure that we can treat like a system of linear equations.
Each system given below is linear in form....

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