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Unformatted text preview: 4. Identify systems that do not have exactly one ordered-pair solution. :I. t- i
.1' x "i % 3: Exactly rmc sulmiun Nu Ltrultllinn [parallel ling-s] Infinitely mnn‘t‘ mitttiuns
t: lines cmncitlt‘i The Numb-er of Stilutinns in a System nf’l‘wn Linear Equations The number of solutions to a system of two linear equations in twn variables is
given by one of the follnwing. (See Figure 5.3.) — Illlllll'ﬂr Suulus H H u H H IIISMGHH'S Gmllilﬂi" I Exactly one ordered pair solutinn The two lines intersect atone point. Infinitely many salutinns The two- iines are parnilel.
The two lines are identical. A linear system that has at least one solution is called a consistent
system. Lines that intersect and lines that coincide both represent
consistent systems. If lines coincide, then the consistent system has
infinitely many solutions, represented by every point on either line.
The equations in a linear system with infinitely many solutions are
called dependent. When you solve by substitution or addition, you will eliminate both variables. However, a true statement, such as
10:10, will be the result. 5. Solve problems using systems of linear equations. Revenue and Cast. Functions
:3. company produces and sells .1: units of a product.
m1?) = (price- pcr unit soldjx
C-[grj ﬁxed. cost 4- [cost per unit prtiducedjx
The Proﬁt Function
The proﬁt, PU), generated after producing and selling .1' units of a product is
given by the proﬁt function
Pﬁx) = RU) — Cir},
where R and (T are the revenue and cost function; respectively. A company is planning to produce a new product. Fixed cost will be $50,000
and it will cost $200 to produce each item. Each item will be sold for $600.
Determine the break~even point for the company on this new product. C(x): Solooo-l-QVDX
RCX): 600)( 600% : 60,000+2mx [(—D'DX : €0,000 X1135” ...
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This note was uploaded on 01/16/2012 for the course MATH 126 taught by Professor Blisinhestiyas during the Fall '11 term at Truckee Meadows Community College.
- Fall '11