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**Unformatted text preview: **Lesson 31
System of equations:
- two or more equations containing common variables
- Example:
- 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 (
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. We will cover substitution in this lesson and elimination in
the next.
Method of Substitution:
1. solve one equation for one variable (it doesn’t matter which equation
you choose or which variable you choose).
2. substitute the solution from step 1 into the other equation.
3. solve the new equation from step 2.
4. back substitute to solve the equation from step 1.
You can verify whether your solution is correct by plugging the ordered
pairs back into the original equations. If the ordered pairs in your solution
set make both of the original equations true, they are correct; if not, they
are incorrect. Example 1: Use the method of substitution to solve the following
systems. Keep in mind, it makes no difference which variable you solve
for, or equation you choose to solve.
a. { b. { c. { d. { e. { f. { Example 2: A cylindrical tube is to be made from a sheet of paper that has
an area of
. Is it possible to construct a tube that has a volume of
? If so, find and . ...

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