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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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Presentation on theme: "LINEAR SYSTEMS Ch. 3.2 Solving Systems Algebraically EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY."— Presentation transcript:

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

2 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.

3 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.

4 SOLVE BY SUBSTITUTION EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

5 SOLVE BY SUBSTITUTION EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

6 SOLVING BY SUBSTITUTION Now you try… EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

7 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.

8 SOLVING BY ELIMINATION EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

9 SOLVING BY ELIMINATION Now you try… EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

10 SOLVING AN EQUIVALENT SYSTEM EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

11 SOLVING AN EQUIVALENT SYSTEM Now you try… EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

12 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.

13 HOMEWORK WB pg. 63 (2-18 EVEN) DUE THURSDAY EQ: HOW CAN I SOLVE SYSTEMS ALGEBRAICALLY? I WILL SOLVE SYSTEMS ALGEBRAICALLY.

14 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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