**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

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.

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

additive inverse

.

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

. Then, check your solution.

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

LEARNING TASKS:

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

LEARNING TASKS:

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.

LEARNING TASKS:

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