Presentation is loading. Please wait.

Presentation is loading. Please wait.

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Similar presentations


Presentation on theme: "Warm Up Problem of the Day Lesson Presentation Lesson Quizzes."— Presentation transcript:

1 Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

2 Solve for the indicated variable. 1. P = R – C for R 2. V = Ah for A
Warm Up Solve for the indicated variable. 1. P = R – C for R 2. V = Ah for A 3. R = for C R = P + C 1 3 = A 3V h C – S t Rt + S = C

3 Problem of the Day At an audio store, stereos have 2 speakers and home-theater systems have 5 speakers. There are 30 sound systems with a total of 99 speakers. How many systems are stereo systems and how many are home-theater systems? 17 stereo systems, 13 home-theater systems

4 Sunshine State Standards
MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations.

5 When solving systems of equations, remember to find values for all of the variables.
Caution!

6 Additional Example 1A: Solving Systems of Equations
Solve the system of equations. y = 4x – 6 y = x + 3 The expressions x + 3 and 4x – 6 both equal y. So by the Transitive Property they are equal to each other. y = 4x – 6 y = x + 3 4x – 6 = x + 3

7 Additional Example 1A Continued
Solve the equation to find x. 4x – 6 = x + 3 – x – x Subtract x from both sides. 3x – 6 = Add 6 to both sides. 3x Divide both sides by 3. = x = To find y, substitute 3 for x in one of the original equations. y = x + 3 = = 6 The solution is (3, 6).

8 Additional Example 1B: Solving Systems of Equations
y = 2x + 9 y = –8 + 2x 2x + 9 = –8 + 2x Transitive Property Subtract 2x from both sides. – 2x – 2x 9 ≠ –8 The system of equations has no solution.

9 Check It Out: Example 1A Solve each system of equations. y = x – 5 y = 2x – 8 x – 5 = 2x – 8 y = x – 5 3 = x y = (3) – 5 = –2 The solution is (3, –2).

10 Check It Out: Example 1B Solve each system of equations. y = 2x y = x + 6 2x = x + 6 y = 2x x = 6 y = 2(6) = 12 The solution is (6, 12).

11 When equations in a system are not already solve for one variable, you can solve both equations for x or both for y.

12 Additional Example 2A: Solving Systems of Equations by Solving for a Variable
Solve the system of equations. x + 4y = – x – 3y = 11 Solve both equations for x. x + 4y = – x – 3y = 11 –4y –4y y y x = –10 – 4y x = y –10 – 4y = y –10 – 4y = y Subtract 3y from both sides. – 3y – 3y –10 – 7y = 11

13 Additional Example 2A Continued
–10 – 7y = 11 Add 10 to both sides. – 7y Divide both sides by –7. –7 = – 7 y = –3 x = y = (–3) Substitute –3 for y. = 11 + –9 = 2 The solution is (2, –3).

14 You can solve for either variable
You can solve for either variable. It is usually easiest to solve for a variable that has a coefficient of 1. Helpful Hint

15 Additional Example 2B: Solving Systems of Equations by Solving for a Variable
Solve the system of equations. –2x + 10y = – x – 5y = 4 Solve both equations for x. –2x + 10y = – x – 5y = 4 –10y –10y y y –2x = –8 – 10y x = 4 + 5y = – –8 –2 10y –2x x = 4 + 5y Subtract 5y from both sides. 4 + 5y = 4 + 5y – 5y – 5y 4 = 4 Since 4 = 4 is always true, the system of equations has an infinite number of solutions.

16 Check It Out: Example 2A Solve each system of equations. 2x + y = 0 2x + 3y = 8 −2x + 8 3 y = −2x and y = −2x + 8 3 –2x = ; x –2 2x + y = 0 2(−2) + y = 0 y = 4 The solution is (–2, 4).

17 Check It Out: Example 2B Solve the system of equations. y = x –1 –3x + 3y = 4 3x + 4 3 y = x − 1 and y = 3x + 4 3 x – 1 = −3 ≠ 4 There are no solutions.

18 Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

19 ( , 2) Lesson Quiz Solve each system of equations. 1. y = 5x + 10
3. 6x – y = –15 2x + 3y = 5 4. Two numbers have a sum of 23 and a difference of 7. Find the two numbers. no solution ( , 2) 1 2 (–2, 3) 15 and 8

20 Lesson Quiz for Student Response Systems
1. Solve the given system of equations. y = 11x + 20 y = –2 + 11x A. (2, 2) B. (1, 1) C. (1, –1) D. no solution

21 Lesson Quiz for Student Response Systems
2. Solve the given system of equations. 4x + y = 11 2x + 3y = –7 A. (4, –5) B. (4, 5) C. (2, –5) D. (2, 5) 21

22 Lesson Quiz for Student Response Systems
3. Two numbers have a sum of 37 and a difference of 17. Identify the two numbers. A. –27 and –10 B. –27 and 10 C. 27 and 10 D. 27 and –10 22


Download ppt "Warm Up Problem of the Day Lesson Presentation Lesson Quizzes."

Similar presentations


Ads by Google