Solving Systems of Equations
What are the three different ways to solve systems of equations?
Graphing, substitution, and elimination
If the lines are parallel (ie their slopes are the same), how many solutions does the system have? What is its classification?
None, Inconsistent
What is the best situation to use substitution?
When one of the variables is solved for
What is the best situation to use elimination?
When coefficients of one variable are the same or the opposite.
The solution to a system of equations should be written as _____________.
An ordered pair (coordinates)
What is the classification of the system if the lines have different slopes?
Consistent and independent
Solve the system of equations by substitution.
y=2x
y=x+4
(4,8)
x+y=3
-x+2y=0
(2,1)
If you want to find the solution to a system of equations visually, which method should you use?
If the lines are the same, what is the classification of the system?
Consistent and dependent
Solve the system of equations by substitution.
y=2
y=x+5
(-3,2)
Solve the system of equations by elimination.
4x+8y=20
-4x+2y=-30
(7,-1)
If one variable is already solved for in a system of equations, which method should you use?
Substitution
How many solutions does this system have?
y=x+7
y=x-7
None
Solve the system of equations by substitution.
-2x-5y=5
y=-3
(5,-3)
Solve the system of equations by elimination.
-4x+9y=9
x-3y=-6
(9,5)
When the coefficients of one variable are the same or opposites, which method should you use?
Elimination
Find the solution to the system of equations by graphing.
y=2x+4
y=-2x+4
(0,4)
Solve the system of equations by substitution.
4x-y=11
-5x-6y=-21
(3,1)
Solve the system of equations by elimination.
5x+4y=-30
3x-9y=-18
(-6,0)