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3.2 Solving Linear Systems Algebraically PowerPoint Presentation

3.2 Solving Linear Systems Algebraically

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### 3.2Solving Linear Systems Algebraically

I can solve a two variable system by substitution.

I can solve a two variable system by elimination.

The Substitution Method

- Step 1:
- Solve one of the equations for one of its variables.

- Step 2:
- Substitute the expression from Step 1 into the other equation and solve for the other variable.

- Step 3:
- Substitute the value from Step 2 into the equation from Step 1 and solve.

Which equation is easiest to get a variable?

Example 1: Substitution3x + 4y = -4

x + 2y = 2

- Step 1: solve for a variable
x + 2y = 2

-2y -2y

x = 2 – 2y

- Step 3: Substitute the value into Step 1
x = 2 – 2(5)

x = 2 – 10

x = -8

- Step 2: Substitute into other equation
3x + 4y = -4

3(2 – 2y) +4y = -4

6 – 6y + 4y = -4

6 – 2y = -4

-6 -6

-2y = -10

-2 -2

y = 5

(-8,5)

The Elimination Method

- Step 1:
- Multiply one or both of the equations by a constant (#) to get both a + and – coefficient for a variable.

- Step 2:
- Add the revised equation(s) from Step 1. By combining like terms, one of your variables will eliminate. Solve for the remaining variable.

- Step 3:
- Substitute the value from Step 2 into either original equation and solve for the other variable.

Which variables are multiples of each other?

Example 2: Elimination (Multiplying 1 Equation)2x – 4y = 13

4x – 5y = 8

- Step 1: Multiply to get a + and – variable.
-2(2x – 4y = 13)

-4x + 8y = -26

- Step 2: Add the revised equation and combine like terms.
-4x + 8y = -26

4x – 5y = 8

3y = -18

3 3

y = -6

Continued….

2x – 4y = 13

4x – 5y = 8

- Step 3: Substitute into an original equation to solve for the other variable.

- y = -6
2x – 4y = 13

2x – 4(-6) = 13

2x + 24 = 13

-24 -24

2x = -11

2 2

x =

(-11/2,-6)

Choose a variable and multiply it by the variable in the other equation.

Example 3: Elimination (Multiplying 2 Equations)7x – 12y = -22

-5x + 8y = 14

Step 1: Multiply to get the same + and – variable.

5(7x – 12y = -22)

35x – 60y = -110

7(-5x + 8y = 14)

-35x + 56y = 98

Step 2: Combine like terms

35x – 60y = -110

-35x + 56y = 98

-4y = -12

-4 -4

y = 3

Continued… other equation.

7x – 12y = -22

-5x + 8y = 14

y = 3

Step 3: Substitute into an original equation

7x – 12y = -22

7x – 12(3) = -22

7x – 36 = -22

+36 +36

7x = 14

7 7

x = 2

(2,3)

Table Partner Classwork other equation.

- Textbook
- Pg 153
- 35-40

- Pg 153
- When you are finished, check with me.
- Start on homework.

- Homework
Solve the system using a chosen method.

- x + 5y = 33
4x + 3y = 13

- -2x + 3y = -13
6x + 2y = 28

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