6.3 Solving Systems Using Elimination

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# 6.3 Solving Systems Using Elimination - PowerPoint PPT Presentation

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?

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### 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?
• 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.
• 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!
Opposites!

Quick Review: Tell me the opposite of each

1. 9

• -30
• 2x
• -28y

-9

30

-2x

28y

Line Up

• Make Opposite
• 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 

Line Up

• Make Opposite
• 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)

Line Up

• Make Opposite
• 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)

Line Up

• Make Opposite
• 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

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)

Wrap Up

• Line up (i.e. Ax + By = C)
• Make opposite