Download Systems of Equations


A system of equations is a set of two or
more equations containing two or more
variables.

A solution of a system of equations with
two variables is the set of ordered pairs
that satisfies each equation in the
system. (There usually is only one!)

We will focus specifically on linear
systems in this unit of study!

The note sheet that you have in front of
you describes three different types of
systems. Your task is to take notes on the
three different scenarios possible when
solving a system of equations.
equations with no common solutions
 expressed as:

› no solution or S = { }
–x+y=3
The lines are
parallel.
y=x– 4
linear equations that intersect in just 1
point.
 Expressed as an order pair
in set notation:

› S = {(x, y)}
S = {(2, 3)}

2 equations with the same graph
› infinite number of solutions
S={real numbers}
Solve the systems listed on your note
sheet. When you are finished, you
should have one example of each
system.
 Remember there are three ways to solve
a system…

We will take a look at each of these in class:
 Systems can be solved by graphing the
system of equations.
 Systems can be solved by substitution where
one equation is substituted into the other.
 Systems can be solved by a process of
called elimination. You must eliminate one
of the variables.
Try either solving by substitution or elimination
on the note sheet.

Elimination (or linearly combinations):
process of multiplying 2 variables by
constants and adding or subtracting the
results. We will call this using linear
combinations to solve a linear system or
elimination (you will hear both terms
used)