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# Copy of Solving System of Equations (Graphing)

MCC9-12.A.REI.6
by

## Joy Crosby

on 4 December 2015

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#### Transcript of Copy of Solving 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 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.

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

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
Full transcript