1. Solving Systems of Equations using Clearboards
Note: The template for the clearboard is the last slide.
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
(MCC9-12.A.REI.1; MCC9-12.A.REI.3; MCC9-12.A.REI.5; MCC9-12.A.REI.6; MCC9-12.A.REI.12; MCC9-12.A.REI.11)

2. -2x + y = 6 +2x +2x y = 2x + 6 -4x + 2(2x+6) = -6 -4x + 4x + 12 = -6
A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions.
Ex: 1
Solve:
Number of solutions:
-2x + y = 6
+2x x
y = 2x + 6
-4x + 2(2x+6) = -6
-4x + 4x + 12 = -6
12 ≠ -6
No solution
Explain why:
Lines
are
parallel

3. One solution (-1, -2) Lines intersect 5(-1) + y = -7 5x + y = -7
A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions.
Ex: 2
Solve:
Number of solutions:
5(-1) + y = -7
-5 + y = -7
y = -2
5x + y = -7
-5x x
y = -5x – 7
x - 4(-5x-7) = 7
x + 20x + 28 = 7
21x + 28 = 7
21x = -21
x = -1
One solution (-1, -2)
Explain why:
Lines
intersect

4. Infinitely many -9x + 3y = -6 +9x +9x 3y = 9x – 6 y = 3x – 2
A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions.
Ex: 3
Solve:
Number of solutions:
-9x + 3y = -6
+9x x
3y = 9x – 6
y = 3x – 2
-3x + (3x – 2) = -2
-2 = -2
Infinitely many
Explain why:
Lines
coincide

5. One solution (1.5, -1) Lines intersect 2(1.5) + 3y = 0 3 + 3y = 0
A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions.
Ex: 4
Solve:
Number of solutions:
2(1.5) + 3y = 0
3 + 3y = 0
3y = -3
y = -1
One solution (1.5, -1)
2x + 3y = 0
-2x x
3y = -2x
y = -2/3x
-2x + 3(-2/3x) = -6
-2x – 2x = -6
-4x = -6
x = 1.5
Explain why:
Lines
intersect

6. -5x -4y = -1 No solution +5x +5x -4y = 5x - 1 y = -5/4x + 1/4
A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions.
Ex: 5
Solve:
Number of solutions:
-5x -4y = -1
+5x x
-4y = 5x - 1
y = -5/4x + 1/4
5x + 4(-5/4x + 1/4) = 2
5x - 5x + 1 = 2
1 ≠ 2
No solution
Explain why:
Lines
are
parallel

7. Solve:
Number of solutions:
Explain why: