Download Four in a Row

Warm Up
Write the following
equations in slopeintercept form.
1) 3y = 6x + 24
2) 2x + y = 20
3.What is the slope of
the line containing the
points (2,2) and (5,5)?
Standard Form
Ax + By = C
Solve for y to rewrite the
equation in slope-intercept form
How do you graph an
equation using the slope
and the y-intercept?
y= mx + b
When all else fails, you can
always make a table and
simply plot points
A solution for a single equation
is ANY point that lies on the line
of that equation
What is a system of
equations?
Let’s look at some examples to
better understand
YES
NO
X+3=5
YES
NO
X+6 ≥ -3
Z+Y < 5
YES
YES
NO
Y=4
Yes or No?
x+y+z= 5
Yes or No?
Yes or No?
X-1> -9x
What is a system of
equations?
Video response
What is a solution to a system
of equations?
Video response
Think-Ink-Share
How do you know that (0,0) is
not the solution to the system
of equations :
3x+y=5 and 2x-1=4
Systems of Linear Equations
• A system of equations is a set of two or more
equations with the same variables.
• A solution to a system of equations is a set of values
for the variables that satisfy all the equations
• The number of equations must match the number of
variables
• A solution for a single linear equation is any point
that lies on the line for that equation. A solution for
a system of linear equations is any point that lies on
each line in the system.
Three Methods for Solving a
System of Equations
• Graphing
• Substitution
• Elimination ( or Linear
Combination)
If I have two lines, is it
possible for them to intersect
at more than one point?
How can you find the solutions of a
system by looking at the graphs?
Systems Applet
EQUATION 1
EQUATION 2
Solution
Sketch the
graphs
Exactly one solution
y
x
Consistent and Independent
System
Exactly one solution
y
x
Infinitely
many
solutions
y
x
Consistent and Dependent
System
Infinitely many solutions
y
x
NO solution
y
x
Inconsistent and Independent
System
NO solution
y
x
You Try
Summary
• How is a system of equations like an
equation? How is it different?
• How can you look at the graph of a system
to find the solution?
Assign Homework:
Clear desk for Ticket Out the Door