Download Concepts 1.1

Bell Work
2/5/14
Solve the system by graphing.
1.
3x  2 y  12

 x  2y  4
3x  2 y  12
 3x
 3x
2 y  3 x  12
2 2 2
3
y  x6
2
3
m
b6
2
x  2y  4
x
x
2 y  x  4
2
2 2
1
y   x 2
2
1
m
b2
2
 2, 3
Yesterday’s Homework
1. Any questions?
2. Please pass your homework to the front.
• Make sure the correct heading is on your paper.
• Is your NAME on your paper?
• Make sure the homework is 100% complete.
• Incomplete work will NOT be accepted.
Heading
5/24/2017
6.2A Solving Systems by
Substitution (isolated)
TSWBAT: solve a linear system by
substitution when a term is already
isolated.
Students solve a system of two linear equations in
two variables algebraically and are able to interpret
the answer graphically. Students are able to solve a
system of two linear inequalities in two variables
and to sketch the solution sets.
Notes
• Solving a System of Equations by Substitution
1. Solve one of the equations for x or y.
- Get x or y by itself.
2. Substitute your new expression from Step 1
into the other equation and solve for the variable.
3. Plug that solved variable into the other equation
from Step 1 and solve for the other variable.
4. Check your answers by plugging it into the
original equations.
Notes
Solve the system by substitution.
Ex.
The variable x is
x  2


x  y  5
already by itself.
x y 5
2  y  5
2
2
y7
2, 7 
1) Solve for
x or y.
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Now you try.
Solve the system by substitution.
Ex.
The variable y is
y4


x  y  2
already by itself.
x y 2
x  4  2
4 4
x6
 6,6, 44
1) Solve for
x or y.
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Solve the system by substitution.
Ex.
The variable x is
x3


2 x  5 y  1
already by itself.
2x  5 y  1
2  3  5 y  1
6  5y  1
6
6
5 y  5
5
5
y  1
3, 1
1) Solve for
x or y.
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Now you try.
Solve the system by substitution.
Ex.
The variable y is
y  1


3x  2 y  8
already by itself.
3x  2 y  8
3x  2 1  8
3x  2  8
2 2
3x  6
3
3
x2
 2,  1
1) Solve for
x or y.
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Solve the system by substitution.
Ex.
The variable y is
 y  2x

 x  y  12
x  y  12
x  2x  12
3x  12
3
3
x4
already by itself.
Step 3
y  2x
y  24 
y 8
 4,4, 88
1) Solve for
x or y.
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Now you try.
Solve the system by substitution.
Ex.
The variable x is
x  3 y


2 x  4 y  4
2 x  4 y  4
2 3 y  4 y  4
6 y  4 y  4
2 y  4
2 2
y2
already by itself.
Step 3
x  3 y
x  3  2 
x  6
 6, 2
1) Solve for
x or y.
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Solve the system by substitution.
Ex.
The variable x is
x  2y 8

already by itself.

2 x  5 y  11
2 x  5 y  11
2 2 y  8  5 y  11
4 y  16  5 y  11
9 y  16  11
16 16
9 y  27
9
9
y  3
1) Solve for
x or y.
Step 3
x  2y 8
x  2 3  8
x  6  8
x2
 2,  3
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Solve the system by substitution.
Ex.
The variable y is
y  3x  4

already by itself.

2 x  2 y  16
1) Solve for
x or y.
2 x  2 y  16
2 x  2 3x  4  16
2x  6x  8  16
8x  8  16
8 8
8x  24
8
Now you try.
8
x  3
Step 3
y  3x  4
y  3 3  4
y 94
y 5
3,3, 55
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Solve the system by substitution.
Ex.
The variable y is
 y  4x  6
already by itself.

 y  2x  4
y  2x  4
 4x  6  2x  4
 2x
 2x
2x  6  4
6 6
2x  10
2
2
x 5
1) Solve for
x or y.
Step 3
y  4x  6
y  4 5   6
y  20  6
y  14
5, 14
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Notes
Solve the system by substitution.
Ex.
The variable y is
 y  3x  5
already by itself.

 y  4x  2
y  4x  2
3x  5  4x  2
 3x
 3x
5  7 x  2
2
2
7  7x
7
7
1  x
Now you try.
1) Solve for
x or y.
Step 3
y  3 x  5
y  3 1  5
y  35
y  2
 1,  2
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Summary
substitution first
To solve a linear system by ___________
identify the isolated variable in one of the equations.
_______
equations to
Next plug that expression into the other _________
find the value of one variable. Finally plug that
equations to find the
solution into any of the original _________
other variable.
Today’s Homework
Rules for Homework
1. Pencil ONLY.
2. Must show all of your work.
• NO WORK = NO CREDIT
3. Must attempt EVERY problem.
4. Always check your answers.
Homework
6.2A
Solve the system by substitution.
x  3
x  4
1.
2.


x  y  8
2 x  3 y  2
4.
 y  2x

x  y  9
7.
x  2 y  5

3x  4 y  5
5.
 x  4 y

 x  y  15
8.
3.
y  3

4 x  2 y  14
6.
 y  3x

2 x  4 y  14
 y  3x  1

2 x  4 y  16
Ticket Out the Door
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Solve the system by substitution.
 x  3

2 x  4 y  10