**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 lines

Solving Systems of equation

is finding

intersections

of 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 and y-Intercept form

Graph

both Equations

2y-x=8

3y-5x-5=0

Now you try it!!

**When you are solving systems, you are, graphically, finding**

intersections

of lines. For two-variable systems, there are then

three

possible types of solutions.

intersections

of 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

Identify the slope and y-intercept .

y= 4x-2 y=-x+3 2y-4x=6

solve systems of equation.

3x-2y=0

3x+y=18

DO NOW

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**