1. Agenda Lesson 6-1 – Solving Systems by Graphing Standards 9.0 Solve a system of two linear equations in two variables and interpret the answer graphically Warm Up Review Notes – Graphing systems Practice Review Homework – Page 576 problems 1 to 3 all

2. Warm Up Write the equation in point-slope form for the line that passes through the given points a. (2, 1) and (4, 4) b. (0, 0) and (2, 4) c.(1, 5) and (2, 3) Homework – Page 576 problems 1 to 3 all

3. Systems System of linear equations– two or more linear equations considered together Solution of a system of linear equations– the ordered pair that satisfies each of the equations in the system.

4. Solving a system of equations EXAMPLE 1 Solve by graphing: y = 2x – 3 y = x – 1 Plot first y-intercept Use slope to plot 2 nd point Connect the points Plot second y-intercept Use slope to plot 2 nd point Connect the points

5. Applications EXAMPLE 2 The system and graph below represent the growth pattern for 2 plants H(d) = 4d + 6 H(d) = 2d + 10 0 1 2 3 4 5 6 7 8 9 4 8 12 16 Height in cm Number of days

6. Interpreting Solutions EXAMPLE 3 Part 1 find the solution by graphing for: H(d) = 4d + 6 H(d) = 2d + 10 The lines intersect at (2, 14) Part 2 Interpret the solution At 2 days, both plants will be the same height, 14 cm tall 0 1 2 3 4 5 6 7 8 9 4 8 12 16 Height in cm Number of days

7. Systems with no solutions EXAMPLE 4 No solution for linear systems means the lines are parallel and do not intersect. y = x – 1 y = x + 2

8. Systems with infinitely Many Solutions EXAMPLE 5 Systems with infinitely many solutions is a system where the lines are the same line y = 2x + 6 4x – 2y = –12

9. Class work – Please do these now Page 279 problems 2 to 22 even Homework – Please do at home tonight Page 576 problems 1 to 3 all