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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?

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

2.

quick review
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.
linear combination addition method elimination
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!
opposites
Opposites!

Quick Review: Tell me the opposite of each

1. 9

  • -30
  • 2x
  • -28y

-9

30

-2x

28y

solve using linear combination

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 

solve using linear combination1

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)

solve using linear combination2

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)

solve using linear combination3

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

application
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
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?