Review: 8.2b Mini-Quiz Find an equation of the line with slope m = 1 and passing through the intersection of the lines x + 7y = 6 and -3x + y = 4.

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Chapter 8 Systems of Linear Equations and Inequalities Lesson 8-3a Solving Systems Equations by Elimination

Objective: Students will learn how to solve a system of linear equations using elimination.

Vocabulary Eliminate Remove or take away

Elimination by Addition Since 3x and –3x are additive inverses, they “disappear” when you add them. Now substitute and find x. Answer: There is one solution (x,y) = (–24, –15). Example 3-1a

Elimination by Subtraction Since 4x and 4x are “same-same”, they “disappear” when you subtract them. 4x + 3y = 18 –4 x – 3y = –18 4x + 3(-10) = 18 4x - 30 = 18 –y = 10 y = –10 4x = 48 Now substitute and find x. x = 12 Answer: There is one solution (x,y) = (12, -10). Example 3-3a` `

What if we can’t do Elimination? Sometimes we can “fix” it by multiplying. Multiply by –2 Now we can use Elimination

Now we can use Elimination Now substitute and find y. Answer: There is one solution (x,y) = (9, 5).

Sometimes we have to multiply twice Now substitute and find x. Answer: There is one solution (x,y) = (–1, 4). Example 4-2a

Determine the best method to solve the system of equations Determine the best method to solve the system of equations. Then solve the system. Multiplying by -3 Example 4-3a

Determine the best method to solve the system of equations Determine the best method to solve the system of equations. Then solve the system. Answer: Subtraction Example 4-3b

Use elimination to solve the system of equations. 3x – 5y = 10 2x – 4y = 4 Answer: There is one solution (x,y) = (10, 4). Example 4-1b

Use elimination to solve the system of equations. 2x – 5y = 11 5x – 2y = – 4

Use elimination to solve the system of equations. Answer: There is one solution (x,y) = (2, 1). Example 3-1b

Use elimination to solve the system of equations. Answer: There is one solution (x,y) = (2, –6). Example 3-3b

Lesson Summary: Objective: Students will learn how to solve a system of linear equations using elimination.

Preview of the next Lesson: Objective: Students will solve real world word problems involving solving systems of equations using elimination.

Homework 465+466/21-33 odd

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