Download A. y

Over Lesson 8–9
Which is an equation for the line of best fit for
the scatter plot where x is the years since 1998
and y is the number of visitors in thousands?
A. y = 3x + 15
B. y = x + 5
C. y = 3x – 15
D.
Use the line of best fit from above to
predict the number of visitors in 2010.
A.
B.
C.
D.
A
B
C
D
You have already solved linear equations by
graphing. (Lesson 8–2)
• Solve systems of linear equations by
graphing.
• Solve systems of linear equations by
substitution.
• system of equations
A set of two or more equations with
the same variables
• substitution Use algebraic methods to find an exact solution of a
system of equations.
Solve by Graphing
Solve the system of equations by graphing.
y = –x + 4
y = 2x + 1
Graph each line.
Solve by Graphing
The graphs appear to intersect at (1, 3). Check this by
replacing x with 1 and y with 3.
Check
y = –x + 4
?
3 = –1 + 4
3 = 3 
y = 2x + 1
?
3 = 2(1) + 1
3 = 3 
Answer: The solution of the system is (1, 3).
What is the solution of the system of equations?
y = –x + 3
y = 4x – 2
A. (2, 1)
B. (2, –1)
C. (1, 2)
D. (1, –2)
A.
B.
C.
D.
A
B
C
D
A. Catori and Mark each download songs. Mark
downloaded 4 times as many songs as Catori. Mark
also downloaded 6 more songs than Catori.
Write a system of equations to represent this
situation.
Let x represent Catori’s songs and y represent Mark’s
songs.
y = 4x
Mark downloaded 4 times as
many songs as Catori.
y = x+6
Mark downloaded 6 more songs
than Catori.
Answer: y = 4x and y = x + 6
B. Catori and Mark each download songs. Mark
downloaded 4 times as many songs as Catori. Mark
also downloaded 6 more songs than Catori.
Solve the system by graphing. Explain what the
solution means.
Graph the equations y = 4x and
y = x + 6 on the same coordinate grid.
The equations intersect at (2, 8).
Answer: So, the solution to the
system is x = 2 and y = 8. This means
that Catori downloaded 2 songs and
Mark downloaded 8 songs.
A. Andy ran twice as far as Ron and Andy ran
8 miles farther than Ron. Which system of
equations represents this situation?
A.
y = 2x
y=x–8
B.
y = 8x
y=x–2
C.
y = 2x
y=x+8
D.
y = 8x
y=x+2
A.
B.
C.
D.
A
B
C
D
B. Andy ran twice as far as Ron and Andy ran
8 miles farther than Ron. How far did each person
run?
A. Andy ran 10 miles.
Ron ran 5 miles.
B. Andy ran 12 miles.
Ron ran 6 miles.
C. Andy ran 16 miles.
Ron ran 8 miles.
D. Andy ran 18 miles.
Ron ran 9 miles.
A.
B.
C.
D.
A
B
C
D
No Solution and Infinitely Many Solutions
A. Solve the system of equations by graphing.
y = –x – 3
2x + 2y = –6
Both equations have the same
graph. Any ordered pair on the
graph will satisfy both
equations.
Answer: Therefore, there are infinitely many solutions
of this system of equations.
No Solution and Infinitely Many Solutions
B. Solve the system of equations by graphing.
y = 2x
y = 2x – 4
The graphs appear to be
parallel lines.
Answer: Since there is no coordinate pair that is a
solution to both equations, there is no solution of this
system of equations.
A. Solve the system of equations by graphing.
y=x+1
2y – 2x = 2
A. (0, 1)
B. (1, 2)
C. infinitely many solutions
D. no solution
A.
B.
C.
D.
A
B
C
D
B. Solve the system of equations by graphing.
y=x
y=x+1
A. (1, 1)
B. (1, 2)
C. infinitely many solutions
D. no solution
A.
B.
C.
D.
A
B
C
D
Solve by Substitution
Solve the system of equations by substitution.
y=7
y = 2x – 5
Replace y with 7 in the second equation.
y = 2x – 5
Write the second equation.
7 = 2x – 5
Replace y with 7.
12 = 2x
6=x
Add 5 to each side.
Solve for x.
Answer: The solution of this system of equations
is (6, 7).
Solve the system of equations by substitution.
y=8
y=x+4
A. (4, 8)
B. (–4, 0)
C. (8, 4)
D. (2, 8)
A.
B.
C.
D.
A
B
C
D