Download 9/28/09 (Monday) NOTES CLASSWORK HOMEWORK System of

9/28/09 (Monday)
NOTES
CLASSWORK
HOMEWORK
System of Equations
 A set of equations for which a
common solution is sought
 A solution of two equations
in two variables is an ordered
pair that makes both
equations true.
CW on Graphing Linear Inequalities
Hw#61
TB p. 338 #27-30
There are three ways to solve a
system of equations.
1) Graphing (the point of
intersection is the solution of
the system)
- If lines have one point of
intersection, that’s the
only solution of the
system.(consistent and
independent)
- If the lines are parallel,
there’s no
solution.(inconsistent)
- If the lines coincide,
there’s an infinite
number of
solutions.(consistent and
dependent)
2) Substitution Method
3) Addition (Elimination)
Method
S.N PH p. 419 #27-30
p. 420 #35-40
Graph on a coordinate plane.
27) 5 x  4 y  20
28) y  1  2 x
29) y  2 x  1
30) y  4 x  0
Write an inequality for each
graph.(You need the textbook for
these problems because there are
graphs you need to see.)
35) (There is a dashed line going
through 1 on the y-axis and the
slope is 1. The right half plane is
shaded)
36) (A solid line goes through -4 on
the y-axis and the slope is 1. Right
side is shaded)
37) (A dashed line goes through -2
on the y-axis and the slope is 1. The
left half plane is shaded)
38) (A solid line goes through 4 on
the y-axis and the slope is 1. The
left half plane is shaded)
39) (A solid line goes through -3 on
the y-axis and the slope is 1. The
right half plane is shaded)
40) (A vertical dashed line passes
through -2 on the x-axis. The right
half plane is shaded)
Match each inequality
with its graph. (You need
to look at the textbook
to do these problems for
there are graphs to look
at.)
27) 2y + x  6
1
x y 4
2
1
29) y  3  x
2
30) 4 y  2 x  16
28)
9/29/09 (Tuesday)
NOTES
CLASSWORK
HOMEWORK
System of Equations
 A set of equations for which a
common solution is sought
 A solution of two equations
in two variables is an ordered
pair that makes both
equations true.
CW on Systems of Equations
Hw#62
TB p. 339 #48-50
There are three ways to solve a
system of equations.
1) Graphing (the point of
intersection is the solution of
the system)
- If lines have one point of
intersection, that’s the
only solution of the
system.(consistent and
independent)
- If the lines are parallel,
there’s no
solution.(inconsistent)
- If the lines coincide,
there’s an infinite
number of
solutions.(consistent and
dependent)
2) Substitution Method
3) Addition (Elimination)
Method
S.N PH p. 360 #1-5, 9-12
Determine whether the given
ordered pair is a solution of the
system of equations.
1) (3,2); 2x + 3y = 12
x - 4y = -5
2) (1,5); 5x - 2y = -5
3x - 7y = -32
3) (3,2); 3t – 2s = 0
t + 2s = 15
4) (2,-2); b + 2a = 2
b – a = -4
5) (-1,1); x = -1
x – y = -2
Solve by Graphing.
9) x + y = 3, x – y = 1
10) x – y = 2, x + y = 6
11) x + 2y = 10, 3x + 4y = 8
12) -3x = 5 – y , 2y = 6x + 10
Write an equation in
slope-intercept from of
the line that passes
through the given point
and is parallel to the
graph of each equation.
48) (1,-3); y = 3x – 2
49) (0,4); x + y = -3
50) (-1,2); 2x – y = 1
9/30/09 (Wednesday)
NOTES
CLASSWORK
HOMEWORK
Solving Systems of Equations Using
the Substitution Method
1) Solve one of the equations
for one of the variables
(x=something or
y=something)
2) Substitute what you solved
for in step 1 in the second
equation and solve. (you
should have only one variable
now).
3) Substitute that value into
either of the original
equations to find the other
value.
4) Check your solution in both
equations.
CW on Systems of Equations
Hw#63
TB p. 255 #1-4
S.N PH p. 362 Try this #a-c,
p.365 #1-4
Solve using the substitution
method.
a. x + y = 5, x = y + 1
b. a – b = 4, b = 2 – 5a
c. y = x + 2, y = 2x – 1
Solve using the substitution
method.
1) x + y = 4, y = 2x + 1
2) x + y = 10, y = x + 8
3) x = y – 1, y = 4 – 2x
4) x = y +6, y = -2 –x
Use the graph to
determine whether each
system has no solution,
one solution, or infinitely
many solutions.
(LOOK AT THE TEXTBOOK
AND DO YOUR WORK.)
10/1/09 (Thursday)
NOTES
No Notes
CLASSWORK
HOMEWORK
CW on Systems of Equations
Hw#64
TB p. 263 # 1-4
Use substitution to solve
each system of equations.
S.N PH p. 365 #5-10, #22-25
Solve using the substitution
method.
5) y = 2x – 5, 3y – x = 5
6) y = 2x + 1, x + y = -2
7) x = -2y, x = 2 – 4y
8) r = -3s, r = 10 – 4s
9) x = 3y – 4, 2x – y = 7
10) s + t = -4, s – t = 2
Translate to a system of equations
and solve.
22) The sum of two numbers is 27.
One number is 3 more than the
other. Find the numbers.
23) The sum of two numbers is 36.
One number is 2 more than the
other. Find the numbers.
24) Find two numbers whose sum
is 58 and whose difference is 16.
25) Find two numbers whose sum
is 66 and whose difference is 8.
1) 2x+7y = 3, x=1-4y
2) 6x – 2y=-4, y=3x+2
3)
y
3
x , 3x-5y=15
5
4) x+3y=12, x-y=8
10/2/09 (Friday)
NOTES
CLASSWORK
HOMEWORK
Solving Systems of Equations Using
the Addition(Elimination) Method
1) Write the equations in
column form with the like
terms in the same column.
2) Make sure the coefficients of
either x or y are
opposites.(Multiply when
necessary.)
3) Add the equations to
eliminate one of the variables
and solve.
4) Substitute that value into
either of the original
equations and find the other
value.
5) Check your solution.
Examples) Solve using the addition
method.
1) x + y = 5, x – y = 1
2) 2x + 3y = 11, -2x + 9y = 1
3) x + 2y = 5, 3x + 2y = 19
CW on Systems of Equations
Hw#65
TB p. 263 # 16 - 19
Use the substitution
method to solve each
system of equations.
16) 3x-5y=11, x-3y=1
17) 2x+3y=1, -x+y/3=5
18) c-5d=2, 2c+d=4
19) 5r-s=5, -4r+5s=17
CW S.N One problem on solving a
system of equations using the
substitution method. (Write
explanation for each step.)
Solve using the substitution
method.
1) 3x + 4y = 2, 2x – y = 5