Download 6.2ab solve systems by substitution

WARM UP (p. 78)
1
For the system, is the
ordered pair a solution
to both equations?!
2
Solve the system by
graphing. How many
solutions? What type of
lines?!
y= x–1
x+y=5
ALGEBRA 1P GAME PLAN
Date
1/5/12 Thursday
Section /
Topic
6-2a: Solving Systems by Substitution (p. 79)
Lesson Goal
STUDENTS WILL BE ABLE TO SOLVE SYSTEMS OF
EQUATIONS BY SUBSTITUTION.
Algebra
California
Standard
9.0 Solve a system of two linear
equations in two variables and interpret
the answer graphically.
Homework
P. 284/ #1-16
P. 286 Checkpoint Quiz 1 #1-10
Announcement
Extra Credit due tomorrow…
THE SUBSTITUTION METHOD!
1
2
3
Solve one of the equations for one of its
variables (if needed).!
Substitute expression from Step 1 into
other equation and solve for other
variable.!
Substitute value from Step 2 into (revised)
equation from Step 1. Solve. !
Example #1: I do it
Use substitution to solve the system of equations.
⎧ 3x + 2y = 8
⎨
⎩ y = x −1
Step 1 Solve one equation for one variable.
Step 2 Substitute the
expression into the other
equation.
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
3x + 2(x – 1) = 8
3x + 2x – 2 = 8
5x – 2 = 8
5x = 10
x = 2
Example #2: We do it Use substitution to solve the system of equations.
Step 1 Solve one equation for one variable.
Step 2 Substitute the
expression into the other
equation.
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
No Solution
Example #3: We do it
Use substitution to solve the system of equations.
-x + y = -1
Step 1 Solve one equation for one variable.
x+y=7
Step 2 Substitute the
expression into the other
equation.
x+y=7
x + (x – 1) = 7
2x – 1 = 7
2x = 8
x=4
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
y=x–1
y = (4) – 1
y=3
The solution is the ordered pair (4, 3).
Warm up Solve the linear system using 1) the substitution method.
3x + y = 4
2x – y = 6
2) Graphing
!
(-1, 5)
ALGEBRA 1P GAME PLAN
Date
1/6/12 Friday
Section /
Topic
6-2b: Solving Systems by Substitution
Lesson Goal
STUDENTS WILL SOLVE SYSTEMS OF EQUATIONS BY
SUBSTITUTION.
Algebra
California
Standard
9.0 Solve a system of two linear
equations in two variables and interpret
the answer graphically.
Homework
PG 284 #(17-21), 24, 25, (29-35 odds), (39-41), (42-50 evens)
Example #4: You do it together
Use substitution to solve the system of equations.
y + 1 = 2x
Step 1 Solve one equation for one variable.
3x + 2y = 26
Step 2 Substitute the
expression into the other
equation.
3x + 2y = 26
3x + 2(2x–1) = 26
3x + 4x – 2 = 26
7x = 28
x=4
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
y = 2x – 1
y = 2(4) – 1
y=7
The solution is the ordered pair (4, 7).
Example #5: You do it together
Use substitution to solve the system of equations.
y=½x+4
Step 1 Solve one equation for one variable.
2x + 2y = 2
Step 2 Substitute the
expression into the other
equation.
2x + 2y = 2
2x + 2(½x + 4) = 2
2x + x + 8 = 2
3x = -6
x = -2
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
y = ½x + 4
y = ½(-2) + 4
y = -1 + 4
y=3
The solution is the ordered pair (-2, 3).
Example #6:
3x-y=13
2x+2y= -10
1.  Solve the 1st eqn for y.
3x-y=13
-y= -3x+13
y=3x-13
2.  Now substitute 3x-13 in
for the y in the 2nd
equation.
2x+2(3x-13)= -10
Now, solve for x.
2x+6x-26= -10
8x=16
x=2
3.  Now substitute the 2 in
for x in for the equation
from step 1.
y=3(2)-13
y=6-13
y=-7
4.  Solution: (2,-7)
Plug in to check soln.
Example #7: You do it together
Use substitution to solve the system of equations.
2y + x = 4
Step 1 Solve one equation for one variable.
3x – 4y = 7
Step 2 Substitute the
expression into the other
equation.
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
Example #8: You do it together
Use substitution to solve the system of equations.
5x + 6y = –9
Step 1 Solve one equation for one variable.
2x – 2 = –y
Step 2 Substitute the
expression into the other
equation.
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
Example #9: You do it alone1
Use substitution to solve the system of equations.
Step 1 Solve one equation for one variable.
Step 2 Substitute the
expression into the other
equation.
Step 3 Substitute the x- or yvalue into one of the original
equations to solve for the
other one.
Lesson Quiz
1
Solve each system using substitution:
Beginners
4x + y = 24
y = –4x + 24
2
Basic
y = 3x – 2
y = –x – 6
(5, 4)
3
Proficient
(-1, -5)
4
Advanced
3x + y = 4
2x – y = 6
(2, -2)
( -1/2 , 0)
Bonus: Use the same system that picked and solve by graphing.