solving systems of equations by graphing. i can: solve systems of equations by graphing determine...
TRANSCRIPT
LESSON 3.1Solving Systems of Equations by
Graphing
Learning Targets:
I can:
Solve systems of equations by graphing
Determine whether a system of equations is consistent and independent, consistent and dependent, or inconsistent.
x + y = 9x – y = 5 }
Two equations together make a system
x = 2, y = 7 or (2, 7)
the solution of the system is the point of intersection.
There are lots of ways to solve system of equations.
Today, you will solve systems of equations by GRAPHING.
Systems of equations…recall that…
EXAMPLE #1 Solve the system by graphing
y = 2x + 3
y = -½ x + 3
Find the coordinates of the point where the lines cross
(0, 3)
Solution: x = 0, y = 3
First, graph y = 2x + 3
Then, graph y = - ½ x + 3
Consistent and Independent?Consistent and Dependent?Inconsistent?
EXAMPLE #2 Solve the system by graphing
3x – 3y = 9
y = -x + 1
-3x -3x
Notice the first equation is not in y = mx + b form.
3x – 3y = 9
– 3y = -3x + 9
-3 -3 -3
y = 1x + -3
EXAMPLE #2 Continued…..
y = 1x + -3
y = -x + 1
Find the coordinates of the point where the lines cross
(2, -1)
Solution: x = 2, y = -1
First, graph y = 1x + -3
Then, graph y = -1x + 1
Consistent and Independent?Consistent and Dependent?Inconsistent?
Solve the system of equations by graphing.
Answer: (4, 1)
Consistent and Independent?Consistent and Dependent?Inconsistent?
Graphing equations with your calculator! 1. Make sure each equation is in y = mx +
b form.
2. Enter equations in y = menu
3. Hit ZOOM then “6” for standard window4. To find the intersection of your
equations, hit:2nd “TRACE”
#5 – “INTERSECT”ENTER
EXAMPLE #3 Solve the system by graphing
y = 2x + 3
y = 2 x – 5
Find the coordinates of the point where the lines cross
Parallel!
No solution (lines don’t intersect)
First, graph y = 2x + 3
Then, graph y = 2x – 5
Consistent and Independent?Consistent and Dependent?Inconsistent?
EXAMPLE #4 Solve the system by graphing
y = -2x + 7
4x + 2y = 14
-4x -4x
Notice the second equation is not in y = mx + b form.
4x + 2y = 14
2y = -4x + 14
2 2 2
y = -2x + 7
Wait! This is the same as the first equation!
EXAMPLE #4 Continued…..
y = -2x + 7
y = -2x + 7
Find the coordinates of the point where the lines cross
They overlap!
Infinitely many solutions
First, graph y = -2x + 7
Then, graph y = -2x + 7
Consistent and Independent?Consistent and Dependent?Inconsistent?
Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
Since the equations are equivalent, their graphs are the same line.
Answer:
Consistent and Independent?Consistent and Dependent?Inconsistent?
Lesson 3.1 Big Idea
Describe the differences between…
Consistent and Independent:
Consistent and Dependent:
Inconsistent:
Assignment
Skills Practice Worksheet
#’s 1 – 6, 10 -12