Questions over hw?

1
Questions over hw?

• Toms Task

2
CCGPS Coordinate AlgebraDay 18 (9-6-12)
UNIT QUESTION How do I justify and solve the
solution to a system of equations or
inequalities? Standard MCC9-12.A.REI.1, 3, 5, 6,
and 12 Todays Question Does multiplying an
equation by a constant change the solution to a
system of equations? Standard MCC9-12.A.REI.5
3
Solve Systems of Equations by Elimination
4
Solve by Graphing
Solution (-1, 3)
5
Analyzing the Solution
Solution (-1, 3)
Does the solution still work if you multiply one
or both of the equations by a number like 2 or -2?
6
Steps for Elimination

1. Arrange the equations with like terms in columns
2. Multiply, if necessary, to create opposite
   coefficients for one variable.
3. Add the equations.
4. Substitute the value to solve for the other
   variable.
5. Check

7
EXAMPLE 1 (continued)
(-1, 3)
8
EXAMPLE 2

• 4x 3y 16
• 2x 3y 8

(4, 0)
9
EXAMPLE 3

• 3x 2y 7
• -3x 4y 5

(1, 2)
10
EXAMPLE 4

• 2x 3y 4
• -4x 5y -8

(2, 0)
11
EXAMPLE 4

• 5x 2y 7
• -4x y 16

(3, -4)
12
EXAMPLE 5

• 2x 3y 1
• 4x 2y 10

(2, -1)
13
Classwork

• Add/Subtract

• Use elimination to solve each system of
  equations.
• 6x 5y 4 2. 3m 4n -14 3. 3a b
  1
• 6x 7y -20 3m 2n -2
  a b 3
• -3x 4y -23 5. x 3y 11 6. x
  2y 6
• -3x y 2 2x 3y 16
  x y 3
• 2a 3b -13 8. 4x 2y 6 9. 5x y 6
• 2a 2b 7 4x 4y 10 5x
  2y 3

(-1, 4)
(-2, 2)
(-1, 2)
(1, 5)
(5, -2)
(4, -1)
(-1/2, 4)
(1/2, 2)
(1, -1)
14
Classwork

• Multiply

• Use elimination to solve each system of
  equations.
• 2x 3y 6 2. 2m 3n 4 3. 3a - b
  2
• x 2y 5 -m 2n 5
  a 2b 3
• 4x 5y 6 5. 4x 3y 22 6.
  3x 4y -4
• 6x - 7y -20 2x y 10
  x 3y -10
• 4x y 9 8. 4a 3b -8 9. 2x 2y 5
• 5x 2y 8 2a 2b 3 4x -
  4y 10

(1, 1)
(-1, 2)
(-3, 4)
(-1, 2)
(4, -2)
(-4, -2)
(2, -1)
(-1/2, 2)
(2.5, 0)
15
Homework

• Practice Worksheet