Download Chapter 2 Lesson 3

Chapter 2
Lesson 3
Systems of Linear Equations
in Two Variables
Different methods of solving System of
Equations in Two Variables
 Graphically/Intersection
 Substitution
 Elimination
Solving a System of Equations Graphically
 Get

both equations into slope-intercept form
Y=mx+b
 Graph



Y= menu
First equation in Y1
Second equation in Y2
 Find



both equations on your calculator
their intersection
2nd Trace
Option 5:intersection
Press ENTER 3 times
 List
X and Y values as an ordered pair
Examples
Solving System of Equations by Substitution
 In
one of the equations, solve for one of the
variables

Doesn’t matter which one, pick whichever is easier
 Substitute
what that variable equals into the second
equation for that variable

Has to be other equation, cannot use same equation
 Solve
for the remaining variable
 Pick an equation to substitute the variable you
solved for, solve for the other variable.

Doesn’t matter which equation, pick the easier one.
Examples
Solving a System of Equations by Elimination
 Multiply
one or both of the equations by a constant
so that one of the variables has the same
coefficient in both equations.
 If the sign in front of the coefficient is the same in
both equations, subtract one equation from the
other.
 If the sign in front of the coefficient is different in
both equations, add the equations together.
 Solve for the remaining variable.
 In one of the equations, substitute the value in for
the variable you solved for, then solve for the
remaining variable.
Examples
Dependent and Inconsistent Systems
A
system of equations has 3 possible outcomes.
 1)The
two equations will intersect at one point and
have a unique solution.
 2)The
two equations will graph the same line
resulting in an infinite number of solutions, this is
called a dependent system.
 3)The
two equations are parallel and will never
intersect, resulting in no solution, this is called an
inconsistent system.
Examples
Homework
 Page
137-141
 1,3,6,9,11,13,15,17,19,21,23,26,31,33,37,38,41,43,
47,49,53,57,63,65