1 / 23

Systems of Equations Problem Solving

Learn to solve systems of equations by finding solutions to varied equations with multiple variables. Practice with examples and discover the importance of solving for all variables.

holmes-meyer
Télécharger la présentation

Systems of Equations Problem Solving

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Systems of Equations 11-6 Course 3 Warm Up Problem of the Day Lesson Presentation

  2. Systems of Equations 11-6 3V = A 1 C – S h 3 t Course 3 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 Rt + S = C

  3. Systems of Equations 11-6 Course 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. Systems of Equations 11-6 Course 3 Learn to solve systems of equations.

  5. Systems of Equations 11-6 Course 3 Insert Lesson Title Here Vocabulary system of equations solution of a system of equations

  6. Systems of Equations 11-6 Course 3 A system of equations is a set of two or more equations that contain two or more variables. A solution of a system of equations is a set of values that are solutions of all of the equations. If the system has two variables, the solutions can be written as ordered pairs.

  7. Systems of Equations 11-6 Caution! When solving systems of equations, remember to find values for all of the variables. Course 3

  8. Systems of Equations 11-6 Course 3 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 equal each other. y= 4x – 6 y =x + 3 4x – 6 = x + 3

  9. Systems of Equations 11-6 Course 3 Additional Example 1A Continued Solve the equation to find x. 4x – 6 = x + 3 – x– x Subtract x from both sides. 3x - 6 = 3 + 6+ 6 Add 6 to both sides. 3x9 Divide both sides by 3. 3 = 3 x = 3 To find y, substitute 3 for x in one of the original equations. y = x + 3 = 3 + 3 = 6 The solution is (3, 6).

  10. Systems of Equations 11-6 Course 3 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.

  11. Systems of Equations 11-6 Course 3 Check It Out: Example 1A Solve the system of equations. y = x – 5 y = 2x – 8 The expressions x – 5 and 2x – 8 both equal y. So by the Transitive Property they equal each other. y=x – 5 y =2x – 8 x – 5 = 2x – 8

  12. Systems of Equations 11-6 Course 3 Check It Out: Example 1A Continued Solve the equation to find x. x – 5 = 2x – 8 – x– x Subtract x from both sides. –5 = x – 8 + 8+ 8 Add 8 to both sides. 3 = x To find y, substitute 3 for x in one of the original equations. y = x – 5 = 3 – 5 = –2 The solution is (3, –2).

  13. Systems of Equations 11-6 Course 3 Check It Out: Example 1B y = 3x + -7 y = 6 + 3x 3x + -7 = 6 + 3x Transitive Property Subtract 3x from both sides. – 3x– 3x -7 ≠ 6 The system of equations has no solution.

  14. Systems of Equations 11-6 Course 3 To solve a general system of two equations with two variables, you can solve both equations for x or both for y.

  15. Systems of Equations 11-6 Course 3 Additional Example 2A: Solving Systems of Equations by Solving for a Variable Solve the system of equations. 5x + y = 7 x – 3y = 11 Solve both equations for x. 5x + y = 7 x – 3y = 11 -y-y+ 3y+ 3y 5x = 7 - y x = 11 + 3y 5(11 + 3y)= 7 -y 55 + 15y = 7 – y Subtract 15y from both sides. - 15y- 15y 55 = 7 – 16y

  16. Systems of Equations 11-6 Course 3 Additional Example 2A Continued 55 = 7 – 16y Subtract 7 from both sides. –7–7 48-16y –16 = -16 Divide both sides by –16. -3 = y x = 11 + 3y = 11 + 3(-3)Substitute –3 for y. = 11 + –9 = 2 The solution is (2, –3).

  17. Systems of Equations 11-6 Helpful Hint You can solve for either variable. It is usually easiest to solve for a variable that has a coefficient of 1. Course 3

  18. Systems of Equations 11-6 = – –8 –2x –2 10y –2 –2 Course 3 Additional Example 2B: Solving Systems of Equations by Solving for a Variable Solve the system of equations. –2x + 10y = –8 x – 5y = 4 Solve both equations for x. –2x + 10y = –8 x – 5y = 4 –10y–10y+5y+5y –2x = –8 – 10yx = 4 + 5y 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.

  19. Systems of Equations 11-6 Course 3 Check It Out: Example 2A Solve the system of equations. x + y = 5 3x + y = –1 Solve both equations for y. x + y = 5 3x + y = –1 –x–x– 3x– 3x y = 5 – x y = –1 – 3x 5 – x = –1 – 3x Add x to both sides. + x+ x 5 = –1 – 2x

  20. Systems of Equations 11-6 Course 3 Check It Out: Example 2A Continued 5 = –1 – 2x + 1+ 1 Add 1 to both sides. 6 = –2x –3 = x Divide both sides by –2. y = 5 – x = 5 – (–3)Substitute –3 for x. = 5 + 3 = 8 The solution is (–3, 8).

  21. Systems of Equations 11-6 Course 3 Check It Out: Example 2B Solve the system of equations. x + y = –2 –3x + y = 2 Solve both equations for y. x + y = –2 –3x + y = 2 – x– x+ 3x+ 3x y = –2 – xy = 2 + 3x –2 – x = 2 + 3x

  22. Systems of Equations 11-6 Course 3 Check It Out: Example 2B Continued –2 – x = 2 + 3x Add x to both sides. + x+ x –2 = 2 + 4x Subtract 2 from both sides. –2–2 –4 = 4x Divide both sides by 4. –1 = x y = 2 + 3x Substitute –1 for x. = 2 + 3(–1) = –1 The solution is (–1, –1).

  23. Systems of Equations 11-6 1 2 ( , 2) Course 3 Insert Lesson Title Here Lesson Quiz Solve each system of equations. 1. y = 5x + 10 y = –7 + 5x 2.y = 2x + 1 y = 4x 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 (–2,3) 15 and 8

More Related