1. CCGPS Coordinate Algebra
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
Today’s Question:
Does multiplying an equation by a constant change the solution to a system of equations?
Standard: MCC9-12.A.REI.5

2. Solve Systems of Equations by Elimination

3. Steps for Elimination:
Arrange the equations with like terms in columns
Multiply, if necessary, to create opposite coefficients for one variable.
Add the equations.
Substitute the value to solve for the other variable.
Check

4. EXAMPLE 1 (continued)
(-1, 3)

5. EXAMPLE 2
4x + 3y = 16 2x – 3y = 8
(4, 0)

6. EXAMPLE 3
3x + 2y = 7 -3x + 4y = 5
(1, 2)

7. EXAMPLE 4
2x – 3y = 4 -4x + 5y = -8
(2, 0)

8. EXAMPLE 5
5x + 2y = 7 -4x + y = –16
(3, -4)

9. EXAMPLE 5
2x + 3y = 1 4x – 2y = 10
(2, -1)

10. Classwork (-1, 4) (-1, 2) (-2, 2) (1, 5) (5, -2) (4, -1) (-1/2, 4)
Add/Subtract
Use elimination to solve each system of equations.
6x + 5y = m – 4n = a + b = 1
6x – 7y = m + 2n = a + b = 3
-3x – 4y = x – 3y = x – 2y = 6
-3x + y = x – 3y = x + y = 3
2a – 3b = x + 2y = x – y = 6
2a + 2b = x + 4y = x + 2y = 3
(-1, 4)
(-1, 2)
(-2, 2)
(1, 5)
(5, -2)
(4, -1)
(-1/2, 4)
(1/2, 2)
(1, -1)

11. Classwork (1, 1) (-3, 4) (-1, 2) (-1, 2) (4, -2) (-4, -2) (2, -1)
Multiply
Use elimination to solve each system of equations.
2x + 3y = m + 3n = a - b = 2
x + 2y = m + 2n = a + 2b = 3
4x + 5y = x – 3y = x – 4y = -4
6x - 7y = x – y = x + 3y = -10
4x – y = a – 3b = x + 2y = 5
5x + 2y = a + 2b = x - 4y = 10
(1, 1)
(-3, 4)
(-1, 2)
(-1, 2)
(4, -2)
(-4, -2)
(2, -1)
(-1/2, 2)
(2.5, 0)

12. Homework
Practice Worksheet