1. Solving a System of Equations in Two Variables By Graphing Chapter 8.1

2. When graphing two equations there are 3 possible scenarios. 1. The two lines could intersect at 1 unique point. (-2, 4)

3. When graphing two equations there are 3 possible scenarios. 2. The two lines could be parallel and never intersect. Inconsistent system of equations No Solution

4. When graphing two equations there are 3 possible scenarios. 3. The two lines could be the same line (coincide). Dependent equations Infinite number of solutions

5. Graphing a system of equations 1. May have to rewrite each equation into y = mx + b. 2. Plot the points and draw each line. 3. Determine the solution.

6. y = mx + b x + y = 12 y = -x + 12 -x -x m = - 1, b = 12 -x + y = 4 +x +x y = x + 4 m = 1, b = 4 1. Solve by graphing.

7. m = - 1, b = 12 m = 1, b = 4 (4, 8) x + y = 12 -x + y = 4 x + y = 12 -x + y = 4 1. Solve by graphing. lines intersect

8. -3 -3 -3 y = mx + b 4x + 2y = 8 2y = -4x + 8 -4x -4x 2 2 2 y = -2x + 4 m = -2, b = 4 -6x – 3y = 6 -3y = 6x + 6 +6x +6x y = -2x – 2 m = -2, b = -2 2. Solve by graphing.

9. x m = - 2, b = 4 m = -2, b = -2 4x + 2y = 8 -6x – 3y = 6 4x + 2y = 8 -6x – 3y = 6 No Solution Inconsistent system of equations 2. Solve by graphing. parallel lines

10. 12 12 12 y = mx + b 3x – 9y = 18 -9y = -3x + 18 -3x -3x -9 -9 -9 y =  x – 2 m = , b = -2 -4x + 12y = -24 12y = 4x – 24 +4x +4x y =  x – 2 m = , b = -2 3. Solve by graphing.

11. m = , b = -2 m = , b = -2 3x – 9y = 18 -4x + 12y = -24 Infinite number of solutions Dependent equations 3x – 9y = 18 -4x + 12y = -24 3. Solve by graphing. lines coincide

12. Solving a System of Equations in Two Variables By Graphing Chapter 8.1