1 / 11

6.3 Solving Systems Using Elimination

6.3 Solving Systems Using Elimination. Standard: SWBAT solve a system of two linear equations in two variables algebraically. Mini Quiz 52. Is (-3, 1) a solution to the System of Equations:. 2. Quick Review. 1 . How do you solve by Substitution?

roary-diaz
Télécharger la présentation

6.3 Solving Systems Using Elimination

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. 6.3 Solving Systems Using Elimination Standard: SWBAT solve a system of two linear equations in two variables algebraically.

  2. Mini Quiz 52 • Is (-3, 1) a solution to the System of Equations: 2.

  3. Quick Review • 1. How do you solve by Substitution? • Pick an equation, substitute, solve, substitute and solve, check • 2. When is the answer “no solution”? • When the graph doesn’t touch or when the equation does not equal. • When is the answer “infinitely many solutions”? • When there is only one graph or when the equation equals on both sides.

  4. Linear Combination…Addition Method…Elimination… • Line up the terms (i.e. Ax + By = C) • Make one of the terms opposite (either the x’s or y’s) • Add the equations (to eliminate one of the variables) • Substitute answer (to find the other variable) • Check!

  5. Opposites! Quick Review: Tell me the opposite of each 1. 9 • -30 • 2x • -28y -9 30 -2x 28y

  6. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination -x + 2y = -8 x + 6y = -16 5. x – 2y = 8 6y + x = -16 x – 2y = 8 x + 6y = -16 -1 8y = -24 y = -3 x – 2y = 8 x – 2(-3) = 8 x + 6 = 8 x = 2 (2, -3) Check (2,-3) x – 2y = 8 2 – 2(-3) = 8 2 + 6 = 8 8 = 8  6y + x = -16 6(-3) + (2) = -16 -18 + 2 = -16 -16 = -16 

  7. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination 6. 4x + 3y = 16 2x – 3y = 8 7. r + t = 1 r – 2t = -2 8. 2m + 5n = -22 10m + 3n = 22 (4, 0) (0,1) (4, -6)

  8. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination 9. -2g + 15h = -32 7g – 5h = 17 10. 4a + 2b = 14 7a – 3b = -8 (1, -2) (1, 5)

  9. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination 11. -x + y = 1 x = y + 1 12. 2x – 4 = -y -2x – y = -4 13. x = -y + 8 y + x + 1= 0 No Solution Infinite Solutions No Solution

  10. Application 14. Suppose your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and solve a system to find the number of each type of ticket sold. a = number of adult tickets s = number of student tickets a + s = 292 3a + 1s = 470 (89, 203)

  11. Wrap Up Elimination (Linear Combination/Addition Method) • Line up (i.e. Ax + By = C) • Make opposite • Add the equations • Substitute answer • Check! No Solution – x and y cancels and both sides are not equal Infinitely Many Solution – x and y cancels and both sides are equal HW: P. 290 #1-6 all, 48, 49, 51-61 odd. DLUQ: What do we need to find in order to eliminate one of the variables?

More Related