Systems%20of%20Linear%20Equations

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Systems of Linear Equations
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Systems of Linear Equations
A system of linear equations is simply two or
more lines graphed on the same graph. They are
also called simultaneous linear equations,
meaning that the graphs of the two lines are
present at the same time.
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Systems of Linear Equations
When two lines are graphed on the same
rectangular coordinate system, three scenarios
are possible The lines can intersect. The
lines can be parallel. The lines can be
coincident (same line)
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Intersecting Lines
If a system has one, or more solutions, it is
said to be consistent. If the lines
intersect the system of equations is
consistent. the equations are
independent. there is exactly one solution an
ordered pair the solution will be the point of
intersection (x, y)
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Coincident Lines
If a system has one, or more solutions, it is
said to be consistent. If the lines are the same
- coincident the system of equations is
consistent. the equations are
dependent. there are infinite solutions all
the points on the lines the solution will be
expressed in set notation. (x, y)x y 6
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Parallel Lines
If a system has no solutions it is said to be
inconsistent. If the lines are parallel the
system of equations is inconsistent. there is
no solution if the solution is expressed in
set notation, it is the empty set.
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Systems of Linear Equations
There is quite a bit of vocabulary involved in
this section. I strongly recommend flash cards!