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# Graphing: System of Equations (Graphing)

MCC9-12.A.REI.6
by

## Mitsouka Jean-Claude

on 3 April 2017

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#### Transcript of Graphing: System of Equations (Graphing)

Solving systems of Linear Equations using Graphing
How to solve...
Y-Intercept Form
y=mx+b
m is slope
b is y-intecept
exercise#1
Write:
Solving Systems of equation
is finding
intersections
of the lines

y=x+2
y=-x-4
1 Solution
Take some notes
exercise #4 Use your graphing calculator
to set up an
xy-chart
for the following two linear functions.Then, solve the system of linear equations.

Write both Linear Equations in
Slope-Intercept form {y=mx+b}
Graph
both Equations
2y-x=8

3y-5x-5=0

Now you try it!!
When you are solving systems
GRAPHICALLY
you are finding
intersection(s)
of the lines. For two-variable systems, there are then
three
possible types of solutions.

x-2y=-2
3x-2y=2
No Solution
Infinite Number of Solutions
One Solution
Where both lines meet is the solution
Ways to simplify 2 equations
Steps...
Solve for X or Y
Then substitute it in the second equation
Collect like terms and simplify.
Steps...
Multiples equation by coefficient to get
.
added together, cancel one of the
variables
Take that value and put it into one of the original equations and
solve for the remaining variable
.
Elimination method
Substitution method
3 solutions of graphs
(-3,-1)
a) what point lies on both lines?
(-3,-1)
(b) Algebraically justify that the point from part (a) is solution to this system of equation by checking to see the point satisfies both equation.
(x,y)= (-3,-1)

y=x+2
-1=-3+2
-1=-1
y=-x-4
-1=-(-3)-4
-1=-1
(x,y)= (-3,-1)
(x,y)= (-3,-1)
Exercise #2: Solve the following system of linear equations by
graphing
each line using the
slope and y-intercept method

y+2x-5=0
y-x=2
slope and y-intercept
y+2x-5=0 y-x=2

Exercise #3: Which of the following is a solution to the system of equations consisting of
y = 4x + 11 and y = −x +1?

(1) (0,11) (3) (−2, 3)

(2) (3, −2 ) (4) (2, 5)

Exercise #4: Alice’s Athletic Arena requires members to pay
\$20 to join and members must pay \$1.50 for each time
they come to work out. Roy’s Romper Room requires members to
pay \$5 to join and members must pay \$4 for each time
they come to work out.
(a) Set up two linear functions for
the cost, C,
of working out at each gym as a function of
the number of times, n,
that a person works out.
Ca=
Cr=

(b) graph both function.
(c) for how many visit n,
will the cost at both gyms be the same?

2y-x=8
3y-5x-5=0
2y-x=8
3y-5x-5=0
What does system means to you? Give as many real-world examples of systems
Speak Out
Equations :

C = 1.50x + 20
C = 4x + 5
Use the Intersection Function
Use the Graphing Calculator to Graph
The Cost is the same at 6 visits
EQ: How does linearity help me to better understand both mathematics as a discipline and the meaning of mathematics in the world?
CQ: How can we use our knowledge of linear equations to solve systems of equations?
March 13, 2017
Announcements
1. Linear Choice Board is due: Wed 3/15
2. Quiz on systems of Equations: Mon. 3/20
The lines intersect at ONLY on point
The lines does NOT intersect at all.
The lines overlap
Examples:
y=
March 24, 2017
Is the point (3,6) a solution to the system of
{x+ 2y= 6 y =3x+2}. Justify your reasoning.

CQ: How can we use our knowledge of linear equations to solve systems of equations using various methods?
EQ: How does linearity help me to better understand both mathematics as a discipline and the meaning of mathematics in the world?(DO NOT COPY)
Announcements
1. Linear Choice Board is due: Immediately. Please email : mjeanclaude@victorycollegiate.org
2. Quiz on systems of Equations: Tomorrow: System of Equations: Graphing and substitution,
GROUP A
Learning OUTCOME:
I can solve systems of Linear Equations Graphically
Guided Notes of Solutions
Solving Systems of Equations(in slope-intercept Form) graphically
Solving System of Equations (in Standard Form)
GROUP B
Learning OUTCOME:
I can solve systems of Linear Equations by Graphing and substitution

Solving System of Equations Graphically(in slope-intercept Form) Graphically.
Solving System of Equations Graphically(in Standard Form) Graphically.
Graphing System of Equations by Substitution

GROUP C
L
earning OUTCOME:
I can solve systems of Linear Equations Algebraically.

1) Graphing systems of Equations( Slope-intercept and Standard Form)
2) Graphing System of Equations by substitution
3) Activities on solving system of Equations by Elimination
WHAT SUCCESS LOOKS LIKE
Write: Parallel lines have no solutions. They do NOT intersect
Example: y= 3x+2
y= 3x+1
What SUCCESS looks like?
Group's Focus:
Solving System of Equations by Graphing
Solving System of Equations by Substitution
CQ: How can we use our knowledge of system of linear equations to solve real-life problems?
EQ: How does linearity help me to better understand both mathematics as a discipline and the meaning of mathematics in the world?(DO NOT COPY)
March 30, 2017
Speak: Please complete the entrance slips.
Announcements:
1. Midterm Friday April 7 2.Choice Board Project is past due. Late due date is Monday
Full transcript