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Lesson 32
System of equations:

two or more equations containing common variables

the solution set of a system is the set containing values of the
variables that satisfy all equations in the system

we will only cover systems with two equation and two variables, so
the solutions will be sets of ordered pairs
( ± ²)
If a system of equations is graphed, the ordered pairs that make up the
solution set are the points where the graphs of the equations intersect.
If the graphs of the equations do not intersect, the system has no solution.
If the equations result in the same graph, the graphs intersect at every
point and there are infinitely many solutions.
The two methods we will use to solve systems are substitution and
elimination.
Substitution was covered in the last lesson and elimination is
covered in this lesson.
Method of Elimination:
1.
multiply at least one equation by a nonzero constant so the
coefficients for one variable will be opposites (same absolute value)
2.
add the equations so the variable with the opposite coefficients will
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