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Bell Work 2/5/14
3 2 121.
2 4
x y
x y
Solve the system by graphing.
1
2m
3
2m
2, 3
2b6b
3 2 12x y 3 3x x
2 3 12y x
2 4x y x x
2 4y x 2 2 2
y 63
2x
2 2 2
y 21
2x
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.
Solving Systems by Substitution (isolated)
04/21/23
Heading
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.
6.2A
Notes• Solving a System of Equations by Substitution
1. Solve one of the equations for x or y.
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.
- Get x or y by itself.
Notes
2
5
x
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable x is already by itself.
5x y 5y 2
2 2
7y
2, 7 2, 7
Notes
4
2
y
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable y is already by itself.
2x y 2x 4
4 4
6x
6, 4 6, 4
Now you try.
Notes
3
2 5 1
x
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable x is already by itself.
2 5 1x y 2 5 1y 3
6 6 5 5y
3, 1 3, 1
6 5 1y
5 51y
Notes
1
3 2 8
y
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable y is already by itself.
3 2 8x y 3 2 8x 1
2 2 3 6x
2, 1 2, 1
3 2 8x
3 32x
Now you try.
Notes
2
12
y x
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable y is already by itself.
12x y 12x 2x
3 12x 3 3
4x
Step 32y x 2y 4
8y
4, 8 4, 8
Notes
3
2 4 4
x y
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable x is already by itself.
2 4 4x y 2 4 4y 3y
6 4 4y y
2 2 2y
Step 33x y 3x 2
6x 2 4y 6, 2 6, 2
Now you try.
Notes
2 8
2 5 11
x y
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable x is already by itself.
2 5 11x y 2 5 11y 2 8y 4 16 5 11y y
9 93y
Step 32 8x y 2 8x 3
9 27y
9 16 11y 16 16
6 8x 2x
2, 3 2, 3
Notes
3 4
2 2 16
y x
x y
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable y is already by itself.
2 2 16x y
2 2 16x 3 4x 2 6 8 16x x
8 83x
Step 33 4y x 3 4y 3
8 24x
8 8 16x 8 8
9 4y 5y
3, 5 3, 5
Now you try.
Notes
4 6
2 4
y x
y x
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable y is already by itself.
2 4y x
2 4x 4 6x
2 25x
Step 34 6y x 4 6y 5
2 10x
2 6 4x 6 6
20 6y 14y
5, 14 5, 14
2 2x x
Notes
3 5
4 2
y x
y x
Ex.
Solve the system by substitution.
2) Substitute into other equation.
3) Plug in answer into other equation.
4) Check answer!
1) Solve for x or y.
The variable y is already by itself.
4 2y x
4 2x 3 5x
7 71 x
Step 33 5y x 3 5y 1
7 7x
5 7 2x 2 2
3 5y 2y
1, 2 1, 2
3 3x x
Now you try.
Summary
To solve a linear system by ___________ first _______ the isolated variable in one of the equations. Next plug that expression into the other _________ to find the value of one variable. Finally plug that solution into any of the original _________ to find the other variable.
substitutionidentify
equations
equations
Today’s Homework
1. Pencil ONLY.2. Must show all of your work.
• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.
Rules for Homework
Homework 6.2A
31.
8
x
x y
Solve the system by substitution.
42.
2 3 2
x
x y
33.
4 2 14
y
x y
24.
9
y x
x y
45.
15
x y
x y
36.
2 4 14
y x
x y
2 57.
3 4 5
x y
x y
3 18.
2 4 16
y x
x y
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Ticket Out the Door
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Solve the system by substitution.
3
2 4 10
x
x y
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