Warm Up

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Warm Up Evaluate each expression for x 1 and y
3. 1. x 4y 2. 2x
y Write each expression in slope-intercept
form. 3. y x 1 4. 2x 3y 6 5. 0 5y 5x

13
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y x 1
y x 2
y x
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Objectives
Identify solutions of linear equations in two
variables. Solve systems of linear equations in
two variables by graphing.
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Vocabulary
systems of linear equations solution of a system
of linear equations
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A system of linear equations is a set of two or
more linear equations containing two or more
variables. A solution of a system of linear
equations with two variables is an ordered pair
that satisfies each equation in the system. So,
if an ordered pair is a solution, it will make
both equations true.
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Example 1A Identifying Solutions of Systems
Tell whether the ordered pair is a solution of
the given system.
(5, 2)
3x y 13
Substitute 5 for x and 2 for y in each equation
in the system.
The ordered pair (5, 2) makes both equations true.
(5, 2) is the solution of the system.
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Example 1B Identifying Solutions of Systems
Tell whether the ordered pair is a solution of
the given system.
x 3y 4
(2, 2)
x y 2
Substitute 2 for x and 2 for y in each equation
in the system.
?
The ordered pair (2, 2) makes one equation true
but not the other.
(2, 2) is not a solution of the system.
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All solutions of a linear equation are on its
graph. To find a solution of a system of linear
equations, you need a point that each line has in
common. In other words, you need their point of
intersection.
The point (2, 3) is where the two lines intersect
and is a solution of both equations, so (2, 3) is
the solution of the systems.
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Example 2A Solving a System by Graphing
Solve the system by graphing. Check your answer.
y x
Graph the system.
y 2x 3
The solution appears to be at (1, 1).
y x

(1, 1)
y 2x 3
The solution is (1, 1).
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Check It Out! Example 2a
Solve the system by graphing. Check your answer.
y 2x 1
Graph the system.
y x 5
The solution appears to be (2, 3).
Check Substitute (2, 3) into the system.
The solution is (2, 3).
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Example 3 Problem-Solving Application
Wren and Jenni are reading the same book. Wren is
on page 14 and reads 2 pages every night. Jenni
is on page 6 and reads 3 pages every night. After
how many nights will they have read the same
number of pages? How many pages will that be?
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Example 3 Continued
Write a system of equations, one equation to
represent the number of pages read by each girl.
Let x be the number of nights and y be the total
pages read.
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Example 3 Continued
Graph y 2x 14 and y 3x 6. The lines
appear to intersect at (8, 30). So, the number of
pages read will be the same at 8 nights with a
total of 30 pages.
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Example 3 Continued
Check (8, 30) using both equations.
Number of days for Wren to read 30 pages.
Number of days for Jenni to read 30 pages.
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Check It Out! Example 3
Video club A charges 10 for membership and 3
per movie rental. Video club B charges 15 for
membership and 2 per movie rental. For how many
movie rentals will the cost be the same at both
video clubs? What is that cost?
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Check It Out! Example 3 Continued
Write a system of equations, one equation to
represent the cost of Club A and one for Club B.
Let x be the number of movies rented and y the
total cost.
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Check It Out! Example 3 Continued
Graph y 3x 10 and y 2x 15. The lines
appear to intersect at (5, 25). So, the cost will
be the same for 5 rentals and the total cost will
be 25.
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Check It Out! Example 3 Continued
Check (5, 25) using both equations.
Number of movie rentals for Club A to reach 25
Number of movie rentals for Club B to reach 25
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Lesson Quiz Part I
Tell whether the ordered pair is a solution of
the given system. 1. (3, 1) 2. (2,
4)
no
yes
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Lesson Quiz Part II
Solve the system by graphing. 3. 4. Joy has
5 collectable stamps and will buy 2 more each
month. Ronald has 25 collectable stamps and will
sell 3 each month. After how many months will
they have the same number of stamps?
How many will that be?
y 2x 9
(2, 5)
y 4x 3
4 months
13 stamps
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Make a Graphic Organizer

• Must fold
• Must have color
• Must write out the problem and include somewhere
  in the organizer
• Must show all 3 methods of solving the problem in
  the organizer
• (Hint All 3 answers should be the same!)

Be Creative!