Download A System of Equations

Notes 5.1
Graphing Systems of
Equations
I. Review: Solutions to Equations
Think Pair Share
• What is a solution to an equation in two
variables?
• What is the connection between an equation
in two variables and it’s graph?
• What is the connection between an equation
and a point on its graph?
• How many solutions does a linear equation
have?
• A solution to an equation in two variables is
any pair of coordinates that makes the
equation true.
• If you plot all of the solutions to a linear
equation on a coordinate plane, they form the
line. All the points on the line are solutions to
the equation- they make the equation true.
• A linear equation as an infinite amount of
solutions- there are an infinite amount of
points on the graph.
II. System of Equations
A. What is it?
A System of Equations:
Two equations with the
same variables, usually
graphed on same coordinate
plane.
y  3x  2
y  x  2
Where do they cross?
(1, 1)
What does that mean?
(1, 1) is the only point that is a
solution to BOTH equations.
2. Types/Number of Solutions
III. Practice
A. Naming Solutions
1. Use the graph to determine whether each system
has no solution, one solution or infinitely many
solutions. If it only has one solution, name it.
One solution: (3, -1)
2. Use the graph to determine whether each system
has no solution, one solution or infinitely many
solutions. If it only has one solution, name it.
Infinitely many
solutions
3. Use the graph to determine whether each system
has no solution, one solution or infinitely many
solutions. If it only has one solution, name it.
No solution
B. Graphing and finding solutions
1. Graph the system of equations. Then determine
whether each system has no solution, one solution or
infinitely many solutions. If the system has one
solution, name it.
One Solution: (-1, -2)
2. Graph the system of equations . Then determine
whether each system has no solution, one solution or
infinitely many solutions. If the system has one
solution, name it.
One Solution: (2, 1)
3. Graph the system of equations . Then determine
whether each system has no solution, one solution or
infinitely many solutions. If the system has one
solution, name it.
Infinitely many solutions
(same line)
3. Graph the system of equations. Then determine
whether each system has no solution, one solution or
infinitely many solutions. If the system has one
solution, name it.
No solution
(parallel lines)