Bell Work
2/6/15
Solve the system by substitution.
1.
x  3


2 x  4 y  6
2x  4 y  6
2 3  4 y  6
6  4 y  6
6
6
4 y  12
4
4
y3
 3, 3
2.
y  2x


3x  4 y  10
3x  4 y  10
3x  4  2x   10
3x  8x  10
5x  10
5 5
x2
y  2x
y  2 2 
y4
 2, 4
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
3/22/2016
6.2B Solving Systems by
Substitution (not isolated)
TSWBAT: solve a linear system by
substitution when first having to
isolate a term.
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.
x  4 y  1
Ex.
 x  4 y  1

2 x  5 y  4
 4y  4y
x  4 y 1
Step 3
2x  5 y  4
2 4 y  1  5 y  4
8y  2  5y  4
3y  2  4
2 2
3y  6
3 3
y2
x  4 y 1
x  4  2  1
x  8 1
x7
 7, 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.
3x  y  2
Ex.
 3x  y  2

4 x  3 y  9
4 x  3 y  9
4 x  3 3x  2  9
4x  9x  6  9
5x  6  9
6 6
5x  15
5
5
x3
 3x
Now you try.
 3x
y  3x  2
Step 3
y  3x  2
y  3  3   2
y  9  2
y  7
 3,  7 
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.
x  3 y  11
Ex.
2 x  4 y  12

 x  3 y  11
 3y  3y
x  3 y  11
Step 3
2 x  4 y  12
2 3 y  11  4 y  12
6 y  22  4 y  12
2 y  22  12
 22  22
2 y  10
2
2
y  5
x  3 y  11
x  3 5  11
x  15 11
x  4
 4,  5
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.
2 x  y  6
Ex.
5 x  2 y  14

2 x  y  6
 2x
 2x
y  2x  6
Step 3
5 x  2 y  14
5x  2  2x  6  14
5x  4x 12  14
x 12  14
 12  12
x  2
y  2x  6
y  2 2  6
y  4  6
y2
2, 2 
Now you try.
1) Solve for
x or y.
2) Substitute
into other
equation.
3) Plug in
answer into
other equation.
4) Check
answer!
Summary
substitution first
To solve a linear system by ___________
isolate the easiest variable in one of the equations.
______
equation to
Next plug that expression into the other ________
solve for one variable. Finally plug that solution into
variable
any of the equations to find the other ________.
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
6.2B
Solve the system by substitution.
 x  2
x  5
1.
2.


x  y  5
2 x  3 y  13
4.
 y  2x  3

2 x  3 y  7
5.
 x  3 y  4

2 x  5 y  6
7.
 x  5 y  13
8.

2 x  4 y  16
4 x  3 y  9

2 x  y  5
3.
 y  2x

3x  5 y  21
6.
 x  2 y  1

4 x  7 y  1
9.
2 x  6 y  2

 x  4 y  15
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.
 4x  y  3

2 x  3 y  19
 2,  5