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LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

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Page 1: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

LINEAR SYSTEMS Ch. 3.2Solving Systems Algebraically

Page 2: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

BELL WORK

Without graphing, determine how many solutions, if any, the system has.

1. X + y = 3, y = 2x – 3

2. X + 2y = 5, 2x + 3y = 9

3. X + 2y = 13, 2y = 7 - x

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 3: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVING SYSTEMS ALGEBRAICALLY

READ

Two algebraic techniques for solving linear systems of equations are substitution and elimination. Both strategies obtain an equation in one variable that can be solved using the Properties of Equality. The resulting value is substituted back into one of the original equations to find the value of the other variable.

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 4: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVE BY SUBSTITUTION

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 5: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVE BY SUBSTITUTION

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 6: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVING BY SUBSTITUTIONNow you try…

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 7: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

STOP AND TALK…

Describe the two strategies that can be used to solve a system of equations. How are they alike? Different?

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 8: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVING BY ELIMINATION

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 9: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVING BY ELIMINATIONNow you try…

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 10: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVING AN EQUIVALENT SYSTEM

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 11: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

SOLVING AN EQUIVALENT SYSTEMNow you try…

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 12: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

STOP AND TALK…

What is an equivalent system?

How can you make a system of equations equivalent?

Why do we have to make a system of equations equivalent when using this strategy?

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

Page 13: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

HOMEWORK

WB pg. 63 (2-18 EVEN) DUE THURSDAY

Page 14: LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY

CLOSURE

(On your bell sheet)

When solving a system of equations, there are many algebraic strategies. Identify the one you feel most

comfortable with. Describe how to use it.

EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

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