System of Equations : A group of two or more
equations .
System of equations in two variables : Two equations in two unknowns.
• Identifying Solutions
A solution of a system of equations in two variables: an ordered pair of
numbers that makes both equations true.
Ex. De termine whether (-1,-2) is a solution of the given system of
equations.
Solving Systems Graphically
Graph both equations and identify any points of intersection.
The coordinates of each point of intersection re present a solution of that
system.
Graphing is not always accurate, so solving by graphing may yield
approximate answers. So check the solution.
When we graph a system of two linear equations in two
variables, one of the fol lowing three outcomes will occur.
1. Graphs intersect at one point.
The system is consistent and has one solution.
Since neither equation is a multiple of the other , they
are independent. |
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2. Graphs are parallel.
The system is inconsistent because
there is no solution.
Since the equations are not equivalent ,
they are independent. |
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3. Equations have the same graph.
The system is consistent and has an infinite
number of solutions.
The equations are dependent since they are
equivalent. |
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Ex. Solve the system graphically.
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Graphing Calculator: use the INTERSECT feature in
the CALC menu
Graphing calculators are useful when equations contain fractions or decimals
or when the coordinates of the intersection are not integers.
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Ex. Solve the system graphically
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Ex. (#56) Deciding whether to purchase or rent a
home is a difficult decision
based on many factors. The graph shows the monthly mortgage payment
($850 per month) compared to the monthly rent payment (initially $600 per
month and raised $50 every six months) for a 1200- square -foot house.
a. If a customer plans to stay only two years (ignoring
any tax benefits),
which costs less per month, renting or buying?
b. After how many months will the monthly rent be the same as the
monthly mortgage payment?
c. In the fourth year, which costs less per month?
d. What other factors should a person consider when deciding whether to
purchase or rent a home?
