9/28/09 (Monday)
NOTES / CLASSWORK / HOMEWORKSystem 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.
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 / CW on Graphing Linear Inequalities
S.N PH p. 419 #27-30
p. 420 #35-40
Graph on a coordinate plane.
27)
28)
29)
30)
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) / Hw#61
TB p. 338 #27-30
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
28)
29)
30)
9/29/09 (Tuesday)
NOTES / CLASSWORK / HOMEWORKSystem 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.
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 / CW on Systems of Equations
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 / Hw#62
TB p. 339 #48-50
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 / HOMEWORKSolving 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
S.N PH p. 362 Try this #a-c,
p.365 #1-4
Solve using the substitution method.
- x + y = 5, x = y + 1
- a – b = 4, b = 2 – 5a
- y = x + 2, y = 2x – 1
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 / Hw#63
TB p. 255 #1-4
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 / CLASSWORK / HOMEWORKNo Notes / CW on Systems 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. / Hw#64
TB p. 263 # 1-4
Use substitution to solve each system of equations.
1)2x+7y = 3, x=1-4y
2)6x – 2y=-4, y=3x+2
3), 3x-5y=15
4)x+3y=12, x-y=8
10/2/09 (Friday)
NOTES / CLASSWORK / HOMEWORKSolving 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
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 / 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